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#+TITLE:    Nomenclature for OpenHPL
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#+AUTHOR:    Dietmar Winkler
#+EMAIL:     dietmar.winkler@usn.no
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* Nomenclature for OpenHPL

| Done    | Component        |     | Type                                | Name                     | Description                                                                                                                                                                                                                                            | Symbol                                |
|---------+------------------+-----+-------------------------------------+--------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------------|
| o       | *Nomenclature*   |     | SI.Area                             | A                        | "*Cross-sectional area*"                                                                                                                                                                                                                               | $A$                                   |
| X       | BendPipe         | -   | SI.Area                             | A                        | "Cross section area"                                                                                                                                                                                                                                   | $A$                                   |
| X       | Reservoir        | -   | SI.Area                             | A                        | "vertiacal cross section"                                                                                                                                                                                                                              | $A$                                   |
| X       | SurgeTank        | -   | SI.Area                             | A                        | "Cross sectional area of the surge tank"                                                                                                                                                                                                               | $A$                                   |
| X       | Fitting          | -   | SI.Area                             | A                        | "Cross section area"                                                                                                                                                                                                                                   | $A$                                   |
| o       | *Nomenclature*   |     | SI.Area                             | A_av                     | "*Average cross-sectional area*"                                                                                                                                                                                                                       | $A_{av}$                              |
| X       | Pipe             |     | SI.Area                             | A_                       | "Average cross section area"                                                                                                                                                                                                                           | $A\_$                                 |
| X       | Drafttube        | -   | SI.Area                             | A_                       | "Average cross-section area of conical diffuser"                                                                                                                                                                                                       | $A\_$                                 |
| -       | PenstockKP       | -   | SI.Area                             | A_atm[N]                 | "centered cross are vector in atm. p."                                                                                                                                                                                                                 |                                       |
| -       | PenstockKP       | -   | SI.Area                             | A_atm_[N + 1]            | "boundary cross are vector in atm. p."                                                                                                                                                                                                                 |                                       |
| -       | PenstockKP       | -   | SI.Area                             | _A_atm[N, 4]             | "boundary cross are matrix in atm. p."                                                                                                                                                                                                                 |                                       |
| o       | *Nomenclature*   |     | SI.Area                             | A_i                      | "*Cross-sectional area of inlet*"                                                                                                                                                                                                                      | $A_i$                                 |
| X       | Pipe             |     | SI.Area                             | A_i                      | "Inlet cross section area"                                                                                                                                                                                                                             | $A_i$                                 |
| X       | Drafttube        | -   | SI.Area                             | A_i                      | "Inlet cross-section area of draft tube"                                                                                                                                                                                                               | $A_i$                                 |
| fixed   | Reservoir        | par | SI.Conversions.NonSIunits.Angle_deg | alpha                    | "The angle of the reservoir walls (zero angle corresponds to vertical walls)"                                                                                                                                                                          | $\alpha$                              |
| -       | Penstock         | -   | SI.Area                             | A_m_end                  |                                                                                                                                                                                                                                                        | $A_{m_{end}}$                         |
| -       | Penstock         | -   | SI.Area                             | A_m_first                |                                                                                                                                                                                                                                                        | $A_{m_{first}}$                       |
| -       | Penstock         | -   | SI.Area                             | A[N]                     |                                                                                                                                                                                                                                                        |                                       |
| -       | PenstockKP       | -   | SI.Area                             | A[N]                     | "centered cross are vector"                                                                                                                                                                                                                            |                                       |
| -       | PenstockKP       | -   | SI.Area                             | A_[N, 4]                 | "boundary cross are vector"                                                                                                                                                                                                                            |                                       |
| o       | *Nomenclature*   |     | SI.Area                             | A_o                      | "*Cross-sectional area of outlet*"                                                                                                                                                                                                                     | $A_o$                                 |
| X       | Pipe             |     | SI.Area                             | A_o                      | "Outlet cross section area"                                                                                                                                                                                                                            | $A_o$                                 |
| X       | Drafttube        | -   | SI.Area                             | A_o                      | "Outlet cross-section area of draft tube"                                                                                                                                                                                                              | $A_o$                                 |
| -       | Penstock         | -   | Real                                | Ap_m[3,N-2]              |                                                                                                                                                                                                                                                        |                                       |
| X       | SurgeTank        | -   | SI.Area                             | A_t                      | "Cross sectional area of the throttle valve surge tank"                                                                                                                                                                                                | $A_t$                                 |
|---------+------------------+-----+-------------------------------------+--------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------------|
| o       | *Numenclature*   |     | SI.Compressibility                  | beta                     | "Compressibility"                                                                                                                                                                                                                                      | $\beta$                               |
| X       | Data             | par | SI.Compressibility                  | beta                     | "Water compressibility"                                                                                                                                                                                                                                | $\beta$                               |
| X       | Data             | par | SI.Compressibility                  | beta_total               | "Total compressibility"                                                                                                                                                                                                                                | $\beta_\text{total}$                  |
| -       | KPOpenChannel    | -   | SI.Height                           | B[N]                     |                                                                                                                                                                                                                                                        | $B[N]$                                |
| -       | KPOpenChannel    | par | SI.Height                           | b[N + 1]                 | "Riverbed"                                                                                                                                                                                                                                             | $b$                                   |
| -       | KPOpenChannel    | par | Boolean                             | boundaryCondition[2, 2]  | "Boundary conditions considering [z_left, q_left; z_right, q_right]", SteadyState = false "If true - starts from Steady State";                                                                                                                        | $$                                    |
| -       | OpenChannel      | par | Boolean                             | BoundaryCondition[2,2]   | "Boundary conditions. Choose options for the boundaries in a matrix table, i.e., if the matrix element = true, this element is used as boundary. The element represent the following quantities: [inlet depth, inlet flow; outlet depth, outlet flow]" | $$                                    |
| o       | *Nomenclature*   | -   | Real                                | cos_theta                | "Slope ratio"                                                                                                                                                                                                                                          | $\cos\theta$                          |
| X       | Pipe             |     | Real                                | cos_theta                | "slope ratio"                                                                                                                                                                                                                                          | $\cos\theta$                          |
| X       | SurgeTank        | -   | Real                                | cos_theta                | "Slope ratio"                                                                                                                                                                                                                                          | $\cos\theta$                          |
| -       | Drafttube        | -   | Real                                | cos_theta                |                                                                                                                                                                                                                                                        | $\cos(\theta)$                        |
| -       | Drafttube        | -   | Real                                | cos_theta_moody          |                                                                                                                                                                                                                                                        | $\cos(\theta_\text{moody})$           |
| -       | Drafttube        | -   | Real                                | cos_theta_moody_by_2     |                                                                                                                                                                                                                                                        | $\frac{\cos(\theta_\text{moody})}{2}$ |
| X       | Data             | par | SI.SpecificHeatCapacity             | c_p                      | "Heat capacity of water at T_0"                                                                                                                                                                                                                        | $c_p$                                 |
|         | SurgeTank        | par | SI.Diameter                         | D                        | "Diameter of the surge shaft"                                                                                                                                                                                                                          | $D$                                   |
| o       | *Nomenclature*   |     | SI.Diameter                         | D_av                     | "Average diameter"                                                                                                                                                                                                                                     | $D_{av}                               |
| X       | Pipe             |     | SI.Diameter                         | D_                       | "Average diameter"                                                                                                                                                                                                                                     | -                                     |
|         | Drafttube        | -   | SI.Diameter                         | D_                       | "Average diameter"                                                                                                                                                                                                                                     | $D_{avg}$                             |
| o       | *Nomenclature*   | -   | SI.Diameter                         | dD                       | "Diameter step"                                                                                                                                                                                                                                        | $\Delta D$                            |
| fixed   | Penstock         | -   | SI.Diameter                         | *dD*  --> D_av           | 0.5 * (D_i + D_o)                                                                                                                                                                                                                                      |                                       |
| X       | PenstockKP       | -   | SI.Diameter                         | dD                       | "step in diameter change"                                                                                                                                                                                                                              |                                       |
| X       | PenstockKP       |     | SI.Length                           | dh                       | "height step"                                                                                                                                                                                                                                          | $\Delta h$                            |
| o       | *Nomenclature*   |     | SI.Diameter                         | D_i                      | "Diameter of the inlet side"                                                                                                                                                                                                                           | $D_i$                                 |
| X       | Pipe             |     | SI.Diameter                         | D_i                      | "Diameter of the inlet side"                                                                                                                                                                                                                           | $D_i$                                 |
| X       | BendPipe         | par | SI.Diameter                         | D_i                      | "Diameter of the inlet side (LHS)"                                                                                                                                                                                                                     | $D_i$                                 |
| X       | Fitting          | par | SI.Diameter                         | D_i                      | "Pipe diameter of the inlet (LHS)"                                                                                                                                                                                                                     | $D_i$                                 |
| X       | Penstock         | par | SI.Diameter                         | D_i                      | "Diametr from *.mothe input side of the pipe"                                                                                                                                                                                                          | $D_i$                                 |
| X       | PenstockKP       | par | SI.Diameter                         | D_i                      | "Diametr from the inlet side of the pipe"                                                                                                                                                                                                              | $D_i$                                 |
| X       | Drafttube        | par | SI.Diameter                         | D_i                      | "Diameter of the inlet side"                                                                                                                                                                                                                           | $D_i$                                 |
| o       | *Nomenclatue*    | -   | SI.Diameter                         | D_c[N]                   | "Centered diameter vector at atm. p"                                                                                                                                                                                                                   | $D_c$                                 |
| X       | Penstock         | -   | SI.Diameter                         | D[N]                     |                                                                                                                                                                                                                                                        | $D[N]$                                |
| X       | PenstockKP       | -   | SI.Diameter                         | D[N] --> D_c[N]          | "centered diameter vector at atm. p."                                                                                                                                                                                                                  | $D_c[N]$                              |
| -       | Penstock         | -   | SI.Diameter                         | D_[N + 1]                | "Boundary diameter vector at atm. p."                                                                                                                                                                                                                  | $D_b$                                 |
| X       | PenstockKP       | -   | SI.Diameter                         | D_[N + 1]                | "Boundary diameter vector at atm. p."                                                                                                                                                                                                                  | $D_b$                                 |
| X       | Pipe             |     | SI.Diameter                         | D_o                      | "Diameter of the outlet side"                                                                                                                                                                                                                          | $D_o$                                 |
| X       | BendPipe         | par | SI.Diameter                         | D_o                      | "Diameter of the outlet side (RHS)"                                                                                                                                                                                                                    | $D_o$                                 |
| X       | Fitting          | par | SI.Diameter                         | D_o                      | "Pipe diameter of the outlet (RHS)"                                                                                                                                                                                                                    | $D_o$                                 |
| X       | Penstock         | par | SI.Diameter                         | D_o                      | "Diametr from the output side of the pipe"                                                                                                                                                                                                             | $D_o$                                 |
| X       | PenstockKP       | par | SI.Diameter                         | D_o                      | "Diametr from the outlet side of the pipe"                                                                                                                                                                                                             | $D_o$                                 |
| X       | Drafttube        | par | SI.Diameter                         | D_o                      | "Diameter of the outlet side, for conical diffuser"                                                                                                                                                                                                    | $D_o$                                 |
| X       | Pipe             |     | SI.Pressure                         | dp                       | "Pressure difference across the pipe"                                                                                                                                                                                                                  | $\Delta p$                            |
| X       | BendPipe         | -   | SI.Pressure                         | dp                       | "Pressure drop of fitting"                                                                                                                                                                                                                             | $\Delta p$                            |
| X       | Fitting          | -   | SI.Pressure                         | dp                       | "Pressure drop of fitting"                                                                                                                                                                                                                             | $\Delta p$                            |
| fixed   | Penstock         | -   | SI.Pressure                         | dp --> dp_N              | "Pressure drop per step"                                                                                                                                                                                                                               | $\Delta p_N$                          |
| removed | PenstockKP       | -   | SI.Pressure                         | dp                       | "initial p. step"                                                                                                                                                                                                                                      | $\Delta p$                            |
| o       | *Nomenclature*   | -   | SI.PressureDifference               | *dp=o.p-i.p*             | "Pressure difference across the pipe"                                                                                                                                                                                                                  | $\Delta p$                            |
| X       | Drafttube        | -   | SI.Pressure                         | *dp*                     | "Pressure drop in and out of draft tube"                                                                                                                                                                                                               | $\Delta p$                            |
| X       | SurgeTank        | par | SI.Diameter                         | D_so                     | "If Sharp orifice type: Diameter of sharp orifice"                                                                                                                                                                                                     | $D_{so}$                              |
| X       | SurgeTank        | par | SI.Diameter                         | D_t                      | "If Throttle value type: Diameter of throat"                                                                                                                                                                                                           | $D_t$                                 |
| X       | Penstock         | -   | SI.Length                           | dx                       |                                                                                                                                                                                                                                                        | $\Delta x$                            |
| X       | PenstockKP       | -   | SI.Length                           | dx                       | "length step"                                                                                                                                                                                                                                          | $\Delta x$                            |
| X       | KPOpenChannel    | -   | SI.Length                           | dx                       |                                                                                                                                                                                                                                                        | $\Delta x$                            |
| X       | Reservoir        | par | Real                                | f                        | "Friction factor of the reservoir"                                                                                                                                                                                                                     | $f$                                   |
| X       | SurgeTank        | -   | SI.Force                            | F                        | "Total force acting in the surge tank"                                                                                                                                                                                                                 | $F$                                   |
| X       | Drafttube        | -   | SI.Force                            | F                        | "Total force acting in the tube"                                                                                                                                                                                                                       | $F$                                   |
|         | Data             | par | SI.Frequency                        | f_0                      | "Initial system frequency"                                                                                                                                                                                                                             | $f_0$                                 |
| X       | PenstockKP       | -   | Real                                | F_[2 * N, 4]             | "F matrix"                                                                                                                                                                                                                                             |                                       |
| X       | KPOpenChannel    | -   | Real                                | F_[2 * N, 4]             | "F matrix"                                                                                                                                                                                                                                             | $F\_$                                 |
| X       | PenstockKP       | -   | Real                                | F_ap[N]                  | "centered A*rho"                                                                                                                                                                                                                                       | $F_{ap}$                              |
| -       | Penstock         | -   | Real                                | F_ap[N-1]                |                                                                                                                                                                                                                                                        |                                       |
| -       | Penstock         | -   | Real                                | F_exp[N]                 |                                                                                                                                                                                                                                                        |                                       |
| -       | Pipe             |     | SI.Force                            | F_f                      | "Friction force"                                                                                                                                                                                                                                       | $F_f$                                 |
| -       | Reservoir        | -   | SI.Force                            | F_f                      | "friction force"                                                                                                                                                                                                                                       | $F_f$                                 |
| -       | SurgeTank        | -   | SI.Force                            | F_f                      | "Friction force"                                                                                                                                                                                                                                       | $F_f$                                 |
| -       | Drafttube        | -   | SI.Force                            | F_f                      | "Fluid frictional force"                                                                                                                                                                                                                               | $F_f$                                 |
| -       | Drafttube        | -   | SI.Force                            | F_fb                     | "Fluid frictional force in the Branch section of Moody spreading pipe"                                                                                                                                                                                 | $F_{fb}$                              |
| -       | Drafttube        | -   | SI.Force                            | F_fm                     | "Fluid frictional force in the Main section of Moody spreading pipe"                                                                                                                                                                                   | $F_{fm}$                              |
| -       | PenstockKP       | -   | SI.Force                            | F_f[N]                   | "centered friction force vector"                                                                                                                                                                                                                       | $F_f[N$]                              |
| -       | KPOpenChannel    | -   | Real                                | F_f[N];                  |                                                                                                                                                                                                                                                        | $F_f$                                 |
| -       | SurgeTank        | -   | SI.Force                            | F_g                      | "Gravity force"                                                                                                                                                                                                                                        | $F_g$                                 |
| -       | Drafttube        | -   | SI.Force                            | F_g                      | "Weight of water"                                                                                                                                                                                                                                      | $F_g$                                 |
| -       | Penstock         | -   | SI.Force                            | F_g[N - 2]               |                                                                                                                                                                                                                                                        | $F_g[N-2]$                            |
| -       | Fitting          | par | Types.Fitting                       | fit_type                 | "Type of pipe fitting";                                                                                                                                                                                                                                | -                                     |
| -       | Penstock         | -   | Real                                | F_m_end                  |                                                                                                                                                                                                                                                        |                                       |
| -       | Penstock         | -   | Real                                | F_m_first                |                                                                                                                                                                                                                                                        |                                       |
| -       | Penstock         | -   | Real                                | F_m[N-2]                 |                                                                                                                                                                                                                                                        |                                       |
| -       | OpenChannel      | par | Real                                | f_n                      | "Manning's roughness coefficient [s/m^1/3]"                                                                                                                                                                                                            | $f_n$                                 |
| -       | KPOpenChannel    | par | Real                                | f_n                      | "Manning's roughness coefficient [s/m^1/3]";                                                                                                                                                                                                           | $f_n$                                 |
| -       | SurgeTank        | -   | SI.Force                            | F_p                      | "Pressure force"                                                                                                                                                                                                                                       | $F_p$                                 |
| -       | Drafttube        | -   | SI.Force                            | F_p                      | "Pressure force"                                                                                                                                                                                                                                       | $F_p$                                 |
| -       | Penstock         | -   | SI.Force                            | F_p[N - 2]               |                                                                                                                                                                                                                                                        | $F_p[N-2]$]                           |
| -       | Data             | par | SI.Acceleration                     | g                        | "Gravity constant"                                                                                                                                                                                                                                     | $g$                                   |
| -       | Data             | par | Real                                | gamma_air                | "Ratio of heat capacities at constant pressure (C_p) to constant volume (C_v) for air at STP"                                                                                                                                                          | $\gamma_\text{air}$                   |
| X       | Pipe             |     | SI.Length                           | H                        | "Height difference from the inlet to the outlet"                                                                                                                                                                                                       | $H$                                   |
| fixed   | Reservoir        | -   | SI.Height                           | H -> h                   | "Water level"                                                                                                                                                                                                                                          | $H$                                   |
| X       | SurgeTank        | par | SI.Height                           | H                        | "Vertical component of the length of the surge shaft"                                                                                                                                                                                                  | $H$                                   |
| X       | SurgeTank        | -   | SI.Height                           | h                        | "Water height in the surge tank"                                                                                                                                                                                                                       | $h$                                   |
| X       | Penstock         | par | SI.Height                           | H                        | "Height over which water fall in the pipe, m"                                                                                                                                                                                                          | $H$                                   |
| X       | PenstockKP       | par | SI.Height                           | H                        | "Height difference from the inlet to the outlet of the pipe"                                                                                                                                                                                           | $H$                                   |
| X       | Drafttube        | par | SI.Length                           | H                        | "Vertical height of conical diffuser"                                                                                                                                                                                                                  | $H$                                   |
|         | SurgeTank        | par | SI.Height                           | h_0                      | "Initial water height in the surge tank"                                                                                                                                                                                                               | $h_0$                                 |
| fixed   | ReservoirChannel | par | SI.Height                           | h0 -> h_0                | "Initial water level of the reservoir";                                                                                                                                                                                                                | $h_0$                                 |
| fixed   | OpenChannel      | par | SI.Height                           | h0[N]-> h_0              | "Initial water level" annotation (Dialog(group = "Initialization"));                                                                                                                                                                                   | $$                                    |
| fixed   | KPOpenChannel    | par | SI.Height                           | h0[N]-> h_0              | "Initial water level"                                                                                                                                                                                                                                  | $h_0$                                 |
| X       | OpenChannel      | par | SI.Height                           | H[2]                     | "Channel bed geometry, height from the left and right sides"                                                                                                                                                                                           | $H[2]$                                |
| X       | KPOpenChannel    | par | SI.Height                           | H[2]                     | "Channel height, left and right side"                                                                                                                                                                                                                  | $H$                                   |
| X       | ReservoirChannel | par | SI.Height                           | H[2]                     | "Reservoir bed height from left and right side";                                                                                                                                                                                                       | $H[2]$                                |
| fixed   | OpenChannel      | -   | SI.Height                           | h[N]                     | "Water level in each unit of the channel"                                                                                                                                                                                                              | $h[N]$                                |
| X       | KPOpenChannel    | -   | SI.Height                           | h[N]                     |                                                                                                                                                                                                                                                        | $$                                    |
| X       | KPOpenChannel    | -   | SI.Height                           | h_[N, 4]                 |                                                                                                                                                                                                                                                        | $$                                    |
| fixed   | Reservoir        | par | SI.Height                           | H_r -> h_0               | "Initial water level above intake"                                                                                                                                                                                                                     | $H_r$                                 |
| X       | PenstockKP       | par | SI.Height                           | h_s0                     | "Initial water head before the pipe, m"                                                                                                                                                                                                                | $H_{s_0}$                             |
| fixed   | Reservoir        | par | Boolean                             | Input_level -> useLevel  | "If checked - the input Level_in should be connected. Otherwise the constant level H_r is used"                                                                                                                                                        | -                                     |
| -       | BendPipe         | par | Real                                | K_L                      | "Loss coefficient for pipe bends (Guess or from manufacturer's design)"                                                                                                                                                                                | $K_L$                                 |
| X       | Pipe             | par | SI.Length                           | L                        | "Length of the pipe"                                                                                                                                                                                                                                   | $L$                                   |
| X       | Reservoir        | par | SI.Length                           | L                        | "Length of the reservoir"                                                                                                                                                                                                                              | $L$                                   |
| X       | SurgeTank        | par | SI.Length                           | L                        | "Length of the surge shaft"                                                                                                                                                                                                                            | $L$                                   |
| X       | SurgeTank        | -   | SI.Length                           | l                        | "Length of water in the surge tank"                                                                                                                                                                                                                    | $l$                                   |
| X       | Fitting          | par | SI.Length                           | L                        | "If Thick Orifice: length of the thick orifice, condition L/D_2<=5. If this condition is not satisfied (L is longer) then use Square Reduction followed by Square Expansion"                                                                           | $L$                                   |
| X       | Penstock         | par | SI.Length                           | L                        | "length of the pipe, m"                                                                                                                                                                                                                                | $L$                                   |
| X       | PenstockKP       | par | SI.Length                           | L                        | "length of the pipe"                                                                                                                                                                                                                                   | $L$                                   |
| X       | Drafttube        | par | SI.Length                           | L                        | "Slant height of conical diffuser, for conical diffuser"                                                                                                                                                                                               | $L$                                   |
| X       | OpenChannel      | par | SI.Length                           | L                        | "Channel length"                                                                                                                                                                                                                                       | $L$                                   |
| X       | KPOpenChannel    | par | SI.Length                           | L                        | "Channel length"                                                                                                                                                                                                                                       | $L$                                   |
| X       | ReservoirChannel | par | SI.Length                           | L                        | "Reservoir length";                                                                                                                                                                                                                                    | $L$                                   |
| -       | PenstockKP       | -   | Real                                | lam1[N, 4]               | "eigenvalue '+'"                                                                                                                                                                                                                                       | $\lambda_+$                           |
| -       | KPOpenChannel    | -   | Real                                | lam1[N, 4]               |                                                                                                                                                                                                                                                        | $\lambda_+$                           |
| -       | PenstockKP       | -   | Real                                | lam2[N, 4]               | "eigenvalue '-'"                                                                                                                                                                                                                                       | $\lambda_-$                           |
| -       | KPOpenChannel    | -   | Real                                | lam2[N, 4]               |                                                                                                                                                                                                                                                        | $\lampda_-$                           |
| -       | Drafttube        | par | SI.Length                           | L_b                      | "Length of Branch section of Moody spreading pipe"                                                                                                                                                                                                     | $L_b$                                 |
| fixed   | Reservoir        | -   | RealInput                           | Level_in -> level        | "Conditional input water level of the reservoir"                                                                                                                                                                                                       | -                                     |
| X       | Drafttube        | par | SI.Length                           | L_m                      | "Length of Main section of Moody spreading pipe"                                                                                                                                                                                                       | $L_m$                                 |
| fixed   | SurgeTank        | par | SI.Diameter -> Length               | L_t                      | "If Throttle value type: +Diameter+ *Length* of throat"                                                                                                                                                                                                | $L_t$                                 |
| X       | Pipe             |     | SI.Mass                             | m                        | "water mass"                                                                                                                                                                                                                                           | $m$                                   |
| X       | Pipe             |     | SI.Momentum                         | M                        | "Water momentum"                                                                                                                                                                                                                                       | $M$                                   |
| X       | Reservoir        | -   | SI.Mass                             | m                        | "water mass"                                                                                                                                                                                                                                           | $m$                                   |
| X       | Reservoir        | -   | SI.Momentum                         | M                        | "water momentum"                                                                                                                                                                                                                                       | $M$                                   |
| X       | SurgeTank        | -   | SI.Mass                             | m                        | "Water mass"                                                                                                                                                                                                                                           | $m$                                   |
| X       | SurgeTank        | -   | SI.Momentum                         | M                        | "Water momuntum"                                                                                                                                                                                                                                       | $M$                                   |
| X       | Drafttube        | -   | SI.Mass                             | m                        | "Mass of water inside conical diffuser"                                                                                                                                                                                                                | $m$                                   |
| X       | Drafttube        | -   | SI.Momentum                         | M                        | "Momentum of water inside the draft tube"                                                                                                                                                                                                              | $M$                                   |
| X       | Data             | par | SI.MolarMass                        | M_a                      | "Molar mass of air at STP"                                                                                                                                                                                                                             | $M_a$                                 |
| X       | SurgeTank        | -   | SI.Mass                             | m_a                      | "Air mass inside surge tank"                                                                                                                                                                                                                           | $m_a$                                 |
| X       | Drafttube        | -   | SI.Mass                             | m_b                      | "Mass of water inside Branch section Moody spreading pipes"                                                                                                                                                                                            | $m_b$                                 |
| X       | ContactPort      |     | SI.MassFlowRate                     | mdot                     | "Mass flow rate"                                                                                                                                                                                                                                       | $\dot{m}$                             |
| X       | Reservoir        | -   | SI.MassFlowRate                     | mdot                     | "water mass flow rate"                                                                                                                                                                                                                                 | $\dot{m}$                             |
| X       | SurgeTank        | -   | SI.Force                            | Mdot                     | "Difference in influent and effulent momentum"                                                                                                                                                                                                         | $\dot{M}$                             |
| X       | Drafttube        | -   | SI.Force                            | Mdot                     | "Rate of change of water momentum"                                                                                                                                                                                                                     | $\dot{M}$                             |
| X       | Drafttube        | -   | SI.MassFlowRate                     | mdot_b                   | "Mass flow rate inside Branch section of Moody spreading pipes"                                                                                                                                                                                        | $\dot{m}_b$                           |
| X       | Penstock         | -   | SI.MassFlowRate                     | mdot_exp[N]              |                                                                                                                                                                                                                                                        | $\dot{m}_{exp}$                       |
| X       | Drafttube        | -   | SI.MassFlowRate                     | mdot_m                   | "Mass flow rate inside Main section of Moody spreading pipes"                                                                                                                                                                                          | $\dot{m}_m$                           |
| X       | PenstockKP       | -   | SI.MassFlowRate                     | mdot[N]                  | "centered mass flow"                                                                                                                                                                                                                                   | $\dot{m}[N]$                          |
| X       | Penstock         | -   | SI.MassFlowRate                     | mdot[N-2]                |                                                                                                                                                                                                                                                        | $\dot{m}[N-2]$                        |
| X       | PenstockKP       | -   | SI.MassFlowRate                     | mdot_[N, 4]              | "boundary mdot matrix";                                                                                                                                                                                                                                | $\mathbf{\dot{m}}$                    |
| X       | Penstock         | -   | SI.MassFlowRate                     | mdot_R                   |                                                                                                                                                                                                                                                        | $\dot{m}_R$                           |
| X       | PenstockKP       | -   | SI.MassFlowRate                     | mdot_R                   | "left bound mdot"                                                                                                                                                                                                                                      | $\dot{m}_R$                           |
| X       | Penstock         | -   | SI.MassFlowRate                     | mdot_V                   |                                                                                                                                                                                                                                                        | $\dot{m}_V$                           |
| X       | PenstockKP       | -   | SI.MassFlowRate                     | mdot_V                   | "right bound mdot"                                                                                                                                                                                                                                     | $\dot{m}_V$                           |
| X       | Drafttube        | -   | SI.Mass                             | m_m                      | "Mass of water inside Main section Moody spreading pipes"                                                                                                                                                                                              | $m_m$                                 |
| X       | Data             | par | SI.DynamicViscosity                 | mu                       | "Dynamic viscosity of water at T_0"                                                                                                                                                                                                                    | $\mu$                                 |
| X       | Penstock         | par | Integer                             | N                        | "Number of segments"                                                                                                                                                                                                                                   | $N$                                   |
| X       | PenstockKP       | par | Integer                             | N                        | "Number of segments"                                                                                                                                                                                                                                   | $N$                                   |
| X       | OpenChannel      | par | Integer                             | N                        | "Number of +discretization units+ *segments*"                                                                                                                                                                                                          | $N$                                   |
| X       | KPOpenChannel    | par | Integer                             | N                        | "Number of segments"                                                                                                                                                                                                                                   | $N$                                   |
| X       | ReservoirChannel | par | Integer                             | N                        | "Number of segments";                                                                                                                                                                                                                                  | $N$                                   |
| X       | Data             | par | SI.Pressure                         | p_a                      | "Atmospheric pressure"                                                                                                                                                                                                                                 | $p_a$                                 |
| X       | SurgeTank        | par | SI.Pressure                         | p_ac                     | "Initial pressure of air-cushion inside the surge tank"                                                                                                                                                                                                | $p_{ac}$                              |
| X       | SurgeTank        | -   | SI.Pressure                         | p_b                      | "Pressure at bottom of the surge tank"                                                                                                                                                                                                                 | $p_b$                                 |
| X       | Pipe             |     | SI.Height                           | p_eps                    | "Pipe roughness height"                                                                                                                                                                                                                                | $p_\epsilon$                          |
| X       | Data             | par | SI.Height                           | p_eps                    | "Pipe roughness height"                                                                                                                                                                                                                                | $p_\epsilon$                          |
| X       | SurgeTank        | par | SI.Height                           | p_eps                    | "Pipe roughness height"                                                                                                                                                                                                                                | $p_\epsilon$                          |
| X       | PenstockKP       | par | SI.Height                           | p_eps                    | "Pipe roughness height"                                                                                                                                                                                                                                | $p_\epsilon$                          |
| X       | Drafttube        | par | SI.Height                           | p_eps                    | "Pipe roughness height"                                                                                                                                                                                                                                | $p_\epsilon$                          |
| fixed   | Penstock         | -   | Real -> SI.Force                    | p_eps_m[N-2] --> F_eps_m |                                                                                                                                                                                                                                                        |                                       |
| fixed   | Penstock         | -   | SI.Length                           | Per_m[N-2]               |                                                                                                                                                                                                                                                        |                                       |
| fixed   | Fitting          | -   | Real                                | phi                      | "Dimensionless factor based on the type of fitting "                                                                                                                                                                                                   | $\phi$                                |
| fixed   | Drafttube        | -   | Real                                | phi_d                    | "Generalized friction factor for draft tube"                                                                                                                                                                                                           | $\phi_d$                              |
| fixed   | Drafttube        | -   | Real                                | phi_d_o                  | "Initial generalized friction factor for Moody spreading pipes"                                                                                                                                                                                        | $\phi_{d_o}$                          |
| fixed   | SurgeTank        | -   | Real                                | phiSO                    | "Dimensionless factor based on the type of fitting "                                                                                                                                                                                                   | $\phi_{SO}$                           |
| fixed   | Pipe             |     | SI.Pressure                         | p_i                      | "Inlet pressure"                                                                                                                                                                                                                                       | $p_i$                                 |
| fixed   | Penstock         | -   | SI.Pressure                         | p_i                      |                                                                                                                                                                                                                                                        | $p_i$                                 |
| fixed   | PenstockKP       | -   | SI.Pressure                         | p_i                      | "Inlet pressure (LHS)"                                                                                                                                                                                                                                 | $p_i$                                 |
| fixed   | Drafttube        | -   | SI.Pressure                         | p_i                      | "Inlet pressure"                                                                                                                                                                                                                                       | $p_i$                                 |
| fixed   | PenstockKP       | par | Boolean                             | PipeElasticity           | "if checked - include pipe elasticity to the model"                                                                                                                                                                                                    |                                       |
| fixed   | Penstock         | -   | SI.Pressure                         | p_m[N-2]                 |                                                                                                                                                                                                                                                        | $p_m[N-2]$                            |
| fixed   | Penstock         | -   | SI.Pressure                         | p_[N-1]                  |                                                                                                                                                                                                                                                        | $p\_[N-1]$                            |
| fixed   | PenstockKP       | -   | SI.Pressure                         | p_[N, 4]                 | "boundary p. matrix";                                                                                                                                                                                                                                  | $\mathbf{p$}                          |
| fixed   | Pipe             |     | SI.Pressure                         | p_o                      | "Outlet pressure"                                                                                                                                                                                                                                      | $p_o$                                 |
| fixed   | Reservoir        | -   | SI.Pressure                         | p_o                      | "outlet pressure"                                                                                                                                                                                                                                      | $p_o$                                 |
| fixed   | Penstock         | -   | SI.Pressure                         | p_o                      |                                                                                                                                                                                                                                                        | $p_o$                                 |
| fixed   | PenstockKP       | -   | SI.Pressure                         | p_o                      | "Outlet Pressure (RHS)"                                                                                                                                                                                                                                | $p_o$                                 |
| fixed   | Drafttube        | -   | SI.Pressure                         | p_o                      | "Outlet pressure"                                                                                                                                                                                                                                      | $p_o$                                 |
| fixed   | PenstockKP       | par | SI.Pressure                         | p_p0                     | "Initial presure vector, bar"                                                                                                                                                                                                                          | $p_{p_0}$                             |
| fixed   | PenstockKP       | -   | SI.Pressure                         | p_p[N]                   | "centered pressure"                                                                                                                                                                                                                                    | $p_p[N]$                              |
| fixed   | SurgeTank        | -   | SI.Pressure                         | p_t                      | "Pressure at top of the surge tank"                                                                                                                                                                                                                    | $p_t$                                 |
| -       | ReservoirChannel | -   | Real                                | q                        |                                                                                                                                                                                                                                                        | $q$                                   |
| -       | KPOpenChannel    | -   | Real                                | q0                       |                                                                                                                                                                                                                                                        | $q_0$                                 |
| -       | KPOpenChannel    | -   | Real                                | q[N]                     |                                                                                                                                                                                                                                                        | $q[N]$                                |
| -       | KPOpenChannel    | -   | Real                                | q_[N, 4]                 |                                                                                                                                                                                                                                                        | $q\_[N,4]$                            |
| -       | KPOpenChannel    | -   | Real                                | q_t;                     |                                                                                                                                                                                                                                                        | $q_t$                                 |
| X       | Data             | par | SI.Density                          | rho                      | "Water density at T_0"                                                                                                                                                                                                                                 | $\rho$                                |
| X       | Penstock         | -   | SI.Density                          | rho_m_end                |                                                                                                                                                                                                                                                        | $\rho_{m_{end}}$                      |
| X       | Penstock         | -   | SI.Density                          | rho_m_first              |                                                                                                                                                                                                                                                        | $\rho_{m_{first}}$                    |
| X       | Penstock         | -   | SI.Density                          | rho_m[N - 2]             |                                                                                                                                                                                                                                                        | $\rho_m$                              |
| X       | PenstockKP       | -   | SI.Density                          | rho[N]                   | "centered density"                                                                                                                                                                                                                                     | $\rho[N]$                             |
| X       | PenstockKP       | -   | SI.Density                          | rho_[N, 4]               | "boundary density"                                                                                                                                                                                                                                     | $\rho\_[N,4]$                         |
| X       | PenstockKP       | -   | Real                                | S_[2 * N]                | "source term"                                                                                                                                                                                                                                          |                                       |
| X       | KPOpenChannel    | -   | Real                                | S_[2 * N]                |                                                                                                                                                                                                                                                        | $S\_$                                 |
| fixed   | Data             | par | Boolean                             | Steady -> SteadyState    | "If checked, simulation starts in Steady State"                                                                                                                                                                                                        | -                                     |
| fixed   | Pipe             | par | Boolean                             | SteadyState              | "If true, starts in Steady State"                                                                                                                                                                                                                      | -                                     |
| fixed   | SurgeTank        | par | Boolean                             | SteadyState              | "If true, starts in Steady State"                                                                                                                                                                                                                      | -                                     |
| fixed   | PenstockKP       | par | Boolean                             | SteadyState              | "If true, starts in Steady State"                                                                                                                                                                                                                      |                                       |
| fixed   | Drafttube        | par | Boolean                             | SteadyState              | "If true, starts in Steady State"                                                                                                                                                                                                                      |                                       |
| fixed   | OpenChannel      | par | Boolean                             | SteadyState              | "If true, starts in Steady State"                                                                                                                                                                                                                      | $$                                    |
| fixed   | ReservoirChannel | par | Boolean                             | SteadyState              | "If true, starts in Steady State"                                                                                                                                                                                                                      |                                       |
| -       | Data             | par | SI.Temperature                      | T_0                      | "Initial water temperature"                                                                                                                                                                                                                            | $T_0$                                 |
| -       | SurgeTank        | par | SI.Temperature                      | T_ac                     | "Initial air-cushion temperature"                                                                                                                                                                                                                      | $T_{ac}$                              |
| -       | Data             | par | Boolean                             | TempUse                  | "If checked, the water temperature is not constant"                                                                                                                                                                                                    | -                                     |
| -       | Fitting          | par | SI.Conversions.NonSIunits.Angle_deg | theta                    | "If Tapered fitting: angle of the tapered reduction/expansion"                                                                                                                                                                                         | $\vartheta$                           |
| -       | PenstockKP       | -   | Real                                | theta                    | "Parameter for slope limiter"                                                                                                                                                                                                                          | $\theta$                              |
| X       | Drafttube        | par | SI.Conversions.NonSIunits.Angle_deg | theta                    | "Angle at which conical diffuser is inclined"                                                                                                                                                                                                          | $\theta$                              |
| -       | KPOpenChannel    | -   | Real                                | theta                    |                                                                                                                                                                                                                                                        | $\theta$                              |
| fixed   | Drafttube        | par | Angle_deg -> *Integer*              | theta_moody              | "Angle at which Moody spreading pipes are branched possible value is 15,30,45,60 or 90)"                                                                                                                                                               | $\theta_\text{moody}$                 |
| -       | PenstockKP       | -   | Real                                | U[2 * N]                 | "centered states"                                                                                                                                                                                                                                      |                                       |
| -       | KPOpenChannel    | -   | Real                                | U[2 * N]                 |                                                                                                                                                                                                                                                        | $$                                    |
| -       | PenstockKP       | -   | Real                                | U_[8, N]                 | "boundary states"                                                                                                                                                                                                                                      |                                       |
| -       | KPOpenChannel    | -   | Real                                | U_[8, N]                 |                                                                                                                                                                                                                                                        | $$                                    |
| -       | KPOpenChannel    | -   | Real                                | U_mp[N]                  |                                                                                                                                                                                                                                                        | $$                                    |
| -       | KPOpenChannel    | -   | SI.Velocity                         | u_[N, 4]                 |                                                                                                                                                                                                                                                        | $$                                    |
| -       | KPOpenChannel    | -   | Real                                | U_pm[N]                  |                                                                                                                                                                                                                                                        | $$                                    |
| fixed   | Reservoir        | par | Boolean                             | useInflow                | "If checked - the inlet/outlet flow is used"                                                                                                                                                                                                           | -                                     |
| X       | Pipe             |     | SI.Velocity                         | v                        | "Water velocity"                                                                                                                                                                                                                                       | $\nu$                                 |
| X       | BendPipe         | -   | SI.Velocity                         | v                        | "Water velocity"                                                                                                                                                                                                                                       | $\nu$                                 |
| X       | Reservoir        | -   | SI.Velocity                         | v                        | "water velosity"                                                                                                                                                                                                                                       | $\nu$                                 |
| X       | SurgeTank        | -   | SI.Velocity                         | v                        | "Water velocity"                                                                                                                                                                                                                                       | $\nu$                                 |
| X       | Fitting          | -   | SI.Velocity                         | v                        | "Water velocity"                                                                                                                                                                                                                                       | $\nu$                                 |
| X       | Drafttube        | -   | SI.Volume                           | V                        | "Volume of water inside the draft tube"                                                                                                                                                                                                                | $V$                                   |
| X       | Drafttube        | -   | SI.Velocity                         | v                        | "Water velocity for conical diffuser"                                                                                                                                                                                                                  | $\nu$                                 |
| fixed   | Data             | par | SI.VolumeFlowRate                   | *V_0* -> Vdot_0          | "Initial flow rate through the system"                                                                                                                                                                                                                 | $V_0$                                 |
| X       | Drafttube        | -   | SI.Velocity                         | v_b                      | "Water velocity inside Branch section of Moody spreading pipes"                                                                                                                                                                                        | $v_b$                                 |
| fixed   | Pipe             |     | SI.VolumeFlowRate                   | Vdot                     | "Volume flow rate"                                                                                                                                                                                                                                     | $\dot{V}$                             |
| fixed   | Reservoir        | -   | SI.VolumeFlowRate                   | Vdot                     | "Flow rate through the reservoir"                                                                                                                                                                                                                      | $\dot{V}$                             |
| fixed   | SurgeTank        | -   | SI.VolumeFlowRate                   | Vdot                     | "Volume flow rate"                                                                                                                                                                                                                                     | $\dot{V}$                             |
| fixed   | Drafttube        | -   | SI.VolumeFlowRate                   | Vdot                     | "Volumeteric flow rate"                                                                                                                                                                                                                                | $\dot{V}$                             |
| fixed   | Pipe             |     | SI.VolumeFlowRate                   | Vdot_0                   | "Initial flow rate in the pipe"                                                                                                                                                                                                                        | $\dot{V}_0$                           |
| fixed   | SurgeTank        | par | SI.VolumeFlowRate                   | Vdot_0                   | "Initial flow rate in the surge tank"                                                                                                                                                                                                                  | $\dot{V}_0$                           |
| fixed   | Penstock         | par | SI.VolumeFlowRate                   | Vdot_0                   | "initial flow rate in the pipes"                                                                                                                                                                                                                       | $\dot{V}_0$                           |
| fixed   | PenstockKP       | par | SI.VolumeFlowRate                   | Vdot_0                   | "Initial flow rate in the pipe vectors"                                                                                                                                                                                                                | $\dot{V}_0$                           |
| fixed   | Drafttube        | par | SI.VolumeFlowRate                   | Vdot_0                   | "Initial flow rate in the pipe"                                                                                                                                                                                                                        | $\dot{V}_0$                           |
| fixed   | OpenChannel      | par | SI.VolumeFlowRate                   | Vdot_0                   | "Initial flow rate"                                                                                                                                                                                                                                    | $\dot{V}_0$                           |
| fixed   | KPOpenChannel    | par | SI.VolumeFlowRate                   | Vdot_0                   | "Initial flow rate";                                                                                                                                                                                                                                   | $\dot{V}_0$                           |
| fixed   | Drafttube        | -   | SI.VolumeFlowRate                   | Vdot_b                   | "Volume +teric+ flow rate for Branch section of Moody spreading pipes"                                                                                                                                                                                 | $\dot{V}_b$                           |
| fixed   | Reservoir        | -   | SI.VolumeFlowRate                   | Vdot_i                   | "Inlet flow rate"                                                                                                                                                                                                                                      | $\dot{V}_i$                           |
| -       | PenstockKP       | -   | SI.VolumeFlowRate                   | Vdot[N]                  | "centered volumetric flow"                                                                                                                                                                                                                             | $\dot{V}[N]$                          |
| -       | KPOpenChannel    | -   | SI.VolumeFlowRate                   | Vdot[N];                 |                                                                                                                                                                                                                                                        | $\dot{V}[N]$                          |
| -       | Reservoir        | -   | SI.VolumeFlowRate                   | Vdot_o                   | "outlet flow rate"                                                                                                                                                                                                                                     | $\dot{V}_o$                           |
| -       | Penstock         | -   | SI.Velocity                         | v_exp[N]                 |                                                                                                                                                                                                                                                        | $\nu_{exp}$                           |
| fixed   | Reservoir        | -   | RealInput                           | *V_in* -> inflow         | "Conditional input inflow of the reservoir"                                                                                                                                                                                                            | -                                     |
| fixed   | OpenChannel      | -   | SI.VolumeFlowRate                   | V_in -> Vdot_i           | "inlet flow"                                                                                                                                                                                                                                           | $V_{in}$                              |
| X       | Drafttube        | -   | SI.Velocity                         | v_m                      | "Water velocity inside Main section of Moody spreading pipes"                                                                                                                                                                                          | $v_m$                                 |
| X       | PenstockKP       | -   | SI.Velocity                         | v[N]                     | "centered velocity"                                                                                                                                                                                                                                    | $\nu[N]$                              |
| X       | PenstockKP       | -   | SI.Velocity                         | v_[N, 4]                 | "bounds velocity"                                                                                                                                                                                                                                      | $\nu\_[N,4]$                          |
| fixed   | OpenChannel      | -   | SI.VolumeFlowRate                   | V_out -> Vdot_o          | "outlet flow"                                                                                                                                                                                                                                          | $V_{out}$                             |
| -       | Penstock         | -   | SI.VolumeFlowRate                   | V_p_out_end              |                                                                                                                                                                                                                                                        |                                       |
| -       | Penstock         | -   | SI.VolumeFlowRate                   | V_p_out[N - 2]           |                                                                                                                                                                                                                                                        |                                       |
| fixed   | Reservoir        | par | SI.Length                           | w -> W                   | "Bed width of the reservoir"                                                                                                                                                                                                                           | $w$                                   |
| fixed   | OpenChannel      | par | SI.Length                           | w -> W                   | "Channel width"                                                                                                                                                                                                                                        | $w$                                   |
| fixed   | KPOpenChannel    | par | SI.Length                           | w -> W                   | "Channel width"                                                                                                                                                                                                                                        | $w$                                   |
| fixed   | ReservoirChannel | par | SI.Length                           | w -> W                   | "Reservoir width";                                                                                                                                                                                                                                     | $w$                                   |
| -       | KPOpenChannel    | -   | SI.Height                           | z[N]                     |                                                                                                                                                                                                                                                        | $$                                    |
| -       | KPOpenChannel    | -   | SI.Height                           | z_[N, 4]                 |                                                                                                                                                                                                                                                        | $$                                    |
|         |                  |     |                                     |                          |                                                                                                                                                                                                                                                        |                                       |
