# Diaphragm


## Copyright © EDF 2002 - 2026  
## ThermoSysPro Version 4.2  
This component model is documented in Sect. 13.7 of the ThermoSysPro book.   

# Diaphragm   
   
A diaphragm measures pressure losses to compute mass flow rates.  
For water/steam, the flow regime can be single-phase or homogeneous two-phase flow. This model accounts for friction pressure losses only.  

Following assumptions are made:  
- the diaphragm aperture relies on sharp ridges.  

The friction pressure loss coefficient is calculated using the geometry of the diaphragm. The diaphragm component thus completes the [singular pressure loss](ThermoSysPro.WaterSteam.PressureLosses.SingularPressureLoss), in which the pressure loss coefficient is a single parameter.  

## Modelica component model  

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

## Nomenclature  

| Symbol| Description| Unit| Definition| Modelica name |  
| :----------------- | :----------------------------------- | :------------------------------- | :--------------------------------------------------------------------------- | :----------- |  
| $D$| Diaphragm diameter| $\mathrm{m}$|| D |  
| $h$| 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 |  
| $Re$| Reynolds number|| $\frac{4 \cdot \lvert \dot{m} \rvert}{\pi \cdot D \cdot \mu \cdot \Omega}$ | Re |  
| $Re_{\lim }$| Limiting Reynolds number| $-$| $10^{5}$| Relim |  
| $\zeta_{\zeta}$| Fluid pressure loss| $\mathrm{Pa}$| $P_{\mathrm{i}}-P_{\mathrm{o}}$| deltaP |  
| $\mu$| Friction pressure loss coefficient| $-$|| khi |  
| $\rho$| Fluid dynamic viscosity| $\mathrm{Pa} \mathrm{s}$|| mu |  
| $\Omega$| Fluid density| $\mathrm{kg} / \mathrm{m}^{3}$ || rho |  



## Governing equations  

### Static momentum balance equation  


    
    

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

- Mathematical formulation:   
   
 $$\Delta P=8 \cdot \zeta_{f} \cdot \frac{\dot{m} \cdot \lvert \dot{m} \rvert}{\pi^{2} \cdot D^{4} \cdot \rho}$$  

- Comments:   
   



### Friction pressure loss coefficient  


    
    

- Validity domain:   
   
 $\forall \dot{m}$ with $Re>Re_{lim}$ and $\Omega>0$  

- Mathematical formulation:   
   
 $$\zeta_{f}=\left(\frac{1.707-\Omega}{\Omega}\right)^{2}$$   

- 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. 13.7. Springer Nature Switzerland AG.