# LumpedStraightPipe


## Copyright © EDF 2002 - 2026   
## ThermoSysPro Version 4.2  
This component model is documented in Sect. 13.5 of the ThermoSysPro book.   
# Lumped straight pipe   

The lumped straight pipe models the pressure loss of a fluid circulating inside a pipe. It must be connected to volumes in order to have a complete model featuring mass, energy, and momentum balance equations.  

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 fluid density $\rho$ is assumed constant along the pipe.  


## Modelica component model  

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

## Nomenclature  

| Symbol| Description| Unit| Definition| Modelica name |  
| :------------------------ | :----------------------------------------------------------- | :------------------------------ | :------------------------------------------------------------------------ | :----------- |  
| $A$| Internal cross section of the pipe| $\mathrm{m}^{2}$| $\pi \cdot D^{2} / 4$| A |  
| $D$| Internal diameter of the pipe| $\mathrm{m}$|| D |  
| $g$| Gravity constant| $\mathrm{m} / \mathrm{s}^{2}$ || g |  
| $h$| Fluid specific enthalpy| $\mathrm{J} / \mathrm{kg}$|| h |  
| $L$| Length of the pipe| $\mathrm{m}$|| L |  
| $\dot{m}$| Fluid mass flow rate| $\mathrm{kg} / \mathrm{s}$|| Q |  
| $P_{\mathrm{i}}$| Fluid pressure at the pipe inlet| $\mathrm{Pa}$|| C1.P |  
| $P_{\mathrm{o}}$| Fluid pressure at the pipe outlet| $\mathrm{Pa}$|| C2.P |  
| $R e$| Fluid Reynolds number| $-$| $\frac{4 \cdot \lvert \dot{m} \rvert}{\pi \cdot D \cdot \mu}$| Re |  
| $z_{\mathrm{i}}$| Inlet altitude of the pipe| $\mathrm{m}$|| z1 |  
| $z_{0}$| Outlet altitude of the pipe| $\mathrm{m}$|| z2 |  
| $\Delta P$| Pressure loss of the fluid between the pipe inlet and outlet | $\mathrm{Pa}$| $P_{\mathrm{i}}-P_{\mathrm{o}}$| deltaP |  
| $\Delta P_{\mathrm{f}}$ | Friction pressure loss between the pipe inlet and outlet| $\mathrm{Pa}$|| deltaPf |  
| $\Delta P_{\mathrm{g}}$ | Gravity pressure loss| $\mathrm{Pa}$| $\rho \cdot \mathrm{g} \cdot\left(z_{\mathrm{o}}-z_{\mathrm{i}}\right)$ | - |  
| $\varepsilon$| Pipe roughness| $\mathrm{m}$|| rugosrel |  
| $\Lambda_{\mathrm{f}}$| Friction pressure loss coefficient| $\mathrm{Pa} . \mathrm{s}$|| lam |  
| $\mu$| Fluid dynamic viscosity| $\mathrm{kg} /$|| mu |  
| $\rho$| Fluid density| $\mathrm{m}^{3}$|| rho |  



## Governing equations  

### Dynamic momentum balance equation  


    
    

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

- Mathematical formulation:   
   
 $$\Delta P=\Delta P_{\mathrm{f}}+\Delta P_{\mathrm{g}}+\frac{L}{A} \cdot \frac{\mathrm{d} \dot{m}}{\mathrm{d} t}$$  

- Comments:   
   
 This is valid only if the mass flow rate wavelength is large as compared to the pipe length $L$, i.e. if there is no water hammer effect inside the pipe. It can for instance be used to model water level oscillations in tanks communicating through a pipe.  


### Static momentum balance equation  

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


    
    

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

- Comments:    


### Friction pressure losses  


    
    

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

- Mathematical formulation:   
   
 $$\Delta P_{\mathrm{f}}=\frac{\Lambda_{\mathrm{f}} \cdot L}{D} \cdot \frac{\dot{m} \cdot \lvert \dot{m} \rvert }{2 \cdot A^{2} \cdot \rho}$$  

- Comments:   
   


## 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. 13.5. Springer Nature Switzerland AG.