# Liquid Pressure Recovery Factor

on . Posted in Fluid Dynamics

Liquid pressure recovery factor, abbreviated as $$F_l$$, a dimensionless number, is the ratio of pressure drop that occures between the vena contracta and the upstream pressure.  Depending on valve type, the pressure recovery factor can vary and can usually be found in the valve manufacturers' specs.  It is used in fluid dynamics to quantify the efficiency of pressure recovery in a fluid flow system, typically across a sudden expansion or contraction in a pipe or duct.

When fluid flows through a constricted section of a pipe, like a nozzle, and then expands suddenly into a larger section, there is a change in the fluid's velocity and pressure. The pressure at the expanded section might not fully recover to the original upstream pressure due to energy losses caused by turbulence and other factors.  The liquid pressure recovery factor is a measure of how much of the pressure is recovered after the expansion process.

The ideal pressure recovery represents the maximum possible pressure recovery that would occur if there were no energy losses in the flow.  In reality, due to factors like turbulence, friction, and other flow phenomena, the actual pressure recovery might be lower than the ideal value.  This factor is a way to express this efficiency.  A high $$F_l$$ value, close to 1, indicates efficient pressure recovery, meaning that a substantial portion of the lost pressure is regained.  A low $$F_l$$ value indicates that there's a significant loss of pressure recovery.

The liquid pressure recovery factor is commonly used in engineering and fluid dynamics to evaluate the performance of components like diffusers, nozzles, and other flow elements where pressure recovery is important, such as in HVAC systems, fluid piping systems, and more.

### Liquid Pressure Recovery Factor formula

$$F_l \;=\; \sqrt{ p_1 - p_2\;/\;p_1 - p_{vc} }$$     (Liquid Pressure Recovery Factor)

$$p_1 \;=\; Fl^2 \; p_{vc} - p_2 \;/\; Fl^2 - 1$$

$$p_2 \;=\; p_1 \left( 1 - Fl^2 \right) + Fl^2 \; p_{vc}$$

$$p_{vc} \;=\; p_1 - \left( p_1 - p_2 \right) \;/\; Fl^2$$

### Solve for Fl

 valve inlet upstream pressure, p1 valve outlet downstream pressure, p2 pressure in vena contracta, pvc

### Solve for p1

 llquid pressure recovery factor, Fl pressure in vena contracta, pvc valve outlet downstream pressure, p2

### Solve for p2

 valve inlet upstream pressure, p1 llquid pressure recovery factor, Fl pressure in vena contracta, pvc

### Solve for pvc

 valve inlet upstream pressure, p1 valve outlet downstream pressure, p2 llquid pressure recovery factor, Fl

Symbol English Metric
$$F_l$$ = llquid pressure recovery factor $$dimensionless$$
$$p_1$$  = valve inlet upstream pressure $$lbf\;/\;in^2$$ $$Pa$$
$$p_2$$  = valve outlet downstream pressure $$lbf\;/\;in^2$$ $$Pa$$
$$p_{vc}$$ = pressure in vena contracta $$lbf\;/\;in^2$$ $$Pa$$

Tags: Pressure Valve Sizing