# SingularPressureLoss


## Copyright © EDF 2002 - 2026  
## ThermoSysPro Version 4.2  
This component model is documented in Sect. 13.4 of the ThermoSysPro book.   

# Singular pressure loss   

This component represents generic pressure losses in a pipe or a singularity using a single-friction pressure loss coefficient. It can also represent the pressure losses inside a circuit of connected pipes and singularities with a pressure loss coefficient equivalent to the whole circuit. The [lumped straight pipe](ThermoSysPro.WaterSteam.PressureLosses.LumpedStraightPipe) should be used instead to take that effect into account. For water/steam, the flow regime can be single-phase or homogeneous two-phase flow.  

Following assumptions are made:  
- The flow inside pressure losses is adiabatic. Non-adiabatic pipes must be  
modeled by connecting pressure losses to volumes.  
- The specific enthalpy inside the components is equal to the specific enthalpy at the inlet.  
- The properties of the fluid are computed for the average pressure..  
- Inertia due to momentum inside pipes is neglected.  

The singular pressure loss component is similar to the [pipe pressure loss](ThermoSysPro.WaterSteam.PressureLosses.PipePressureLoss), except that inlet and outlet altitudes of the pipe are pre-defined.  
To model pressure loss in a bent pipe, see [bend](ThermoSysPro.WaterSteam.PressureLosses.Bend).  

## Modelica component model  

The equations mentioned below are implemented in the component *SingularPressureLoss*, located in the *WaterSteam.PressureLosses* sub-library.  
This component has 2 connectors:  
- C1: fluid inlet,  
- C2: fluid outlet.  
   
![ThermoSysPro.WaterSteam.PressureLosses.SingularPressureLoss.svg](./icons/ThermoSysPro.WaterSteam.PressureLosses.SingularPressureLoss.svg)  

## Nomenclature  

| Symbol| Description| Unit| Definition| Modelica name |  
| :------------------------ | :---------------------------------------------------------- | :------------------------------- | :--------------------------------------------------------------- | :----------- |  
| $g$| Gravity constant| $\mathrm{m} / \mathrm{s}^{2}$|| - |  
| $h$| Fluid specific enthalpy | $\mathrm{J} / \mathrm{kg}$|| h |  
| $m$| Fluid mass flow rate| $\mathrm{kg} / \mathrm{s}$|| Q |  
| $P_{\mathrm{i}}$| Fluid pressure at the inlet| $\mathrm{Pa}$|| C1.P |  
| $P_{\mathrm{o}}$| Fluid pressure at the outlet| $\mathrm{Pa}$|| C2.P |  
| $z_{\mathrm{i}}$| Inlet altitude| $\mathrm{m}$|| - |  
| $z_{0}$| Outlet altitude| $\mathrm{m}$|| - |  
| $\Delta P$| Pressure loss of the fluid between the inlet and the outlet | $\mathrm{Pa}$| $P_{\mathrm{i}}-P_{\mathrm{o}}$| deltaP |  
| $\Delta P_{\mathrm{f}}$ | Friction pressure loss between the inlet and the outlet| $\mathrm{Pa}$|| - |  
| $\Delta P_{\mathrm{g}}$ | Gravity pressure loss between the inlet and the outlet| $\mathrm{Pa}$| $\rho \cdot g \cdot\left(z_{\mathrm{o}}-z_{\mathrm{i}}\right)$ | - |  
| $\Lambda$| Friction pressure loss coefficient| $\mathrm{m}^{-4}$|| K |  
| $\rho$| Fluid density| $\mathrm{kg} / \mathrm{m}^{3}$ || rho |  


## Governing equations  

### Static momentum balance equation  


    
    

- Validity domain:   
   
 $\forall \dot{m}$  

- Mathematical formulation:   
   
 $$\Delta P=\Delta P_{\mathrm{f}}+\Delta P_{\mathrm{g}}$$  

- Comments:   
   
 In case of a singularity, $z_{\mathrm{o}}=z_{\mathrm{i}}$ and consequently $\Delta P_{\mathrm{g}}=0$.  


### Friction pressure losses  


    
    

- Validity domain:   
   
 $\forall \dot{m}$  

- Mathematical formulation:   
   
 $$\Delta P_{\mathrm{f}}=\Lambda \cdot \frac{\dot{m} \cdot \lvert \dot{m} \rvert }{\rho}$$  

- Comments:   
   
The pressure loss coefficient $\Lambda$ is provided by the user or can be obtained by inverse calculation from the mass flow rate.  

## References   
   
El Hefni, Baligh and Bouskela, Daniel (2019). [Modeling and Simulation of Thermal Power Plants with ThermoSysPro](https://link.springer.com/book/10.1007/978-3-030-05105-1), sect. 13.4. Springer Nature Switzerland AG.