Liquid Pressure Recovery Factor Formula |
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\( F_l \;=\; \sqrt{ \dfrac{ p_1 - p_2 }{ p_1 - p_{vc} } }\) (Liquid Pressure Recovery Factor) \( p_1 \;=\; \dfrac{ F_l^2 \cdot p_{vc} - p_2 }{ F_l^2 - 1 }\) \( p_2 \;=\; p_1 \cdot \left( 1 - F_l^2 \right) + F_l^2 \cdot p_{vc} \) \( p_{vc} \;=\; \dfrac{ p_1 - \left( p_1 - p_2 \right) }{ F_l^2 } \) |
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| Symbol | English | Metric |
| \( F_l \) = Llquid Pressure Recovery Factor | \(dimensionless\) | \(dimensionless\) |
| \( p_1 \) = Valve Inlet Upstream Pressure | \(lbf\;/\;in^2\) | \(Pa\) |
| \( p_2 \) = Valve Outlet Downstream Pressure | \(lbf\;/\;in^2\) | \(Pa\) |
| \( p_{vc} \) = Pressure in Vena Contracta | \(lbf\;/\;in^2\) | \(Pa\) |
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.
Liquid Pressure Recovery Factor Interpretation
- Valve Performance - In control valves, \( F_l \) reflects how the valve design affects flow behavior. Valves with streamlined paths (globe valves) tend to have higher \( F_l \) values (less recovery), while those with abrupt changes (butterfly valves) have lower \( F_l \) values (more recovery). This is because streamlined designs minimize turbulence losses downstream.
- Cavitation Risk - \( F_l \) is critical for predicting cavitation when the pressure at the vena contracta drops below the fluid’s vapor pressure, forming vapor bubbles that collapse downstream. A lower \( F_l \) (more recovery) reduces cavitation risk because the downstream pressure rises further above the vapor pressure. A higher \( F_l \) increases the risk, as the pressure stays lower longer.
- Flow Capacity - It influences the maximum flow rate through a valve. When the pressure drop is large enough to cause choking (where flow no longer increases with further pressure drop), \( F_l \) helps determine that critical point. A valve with a high \( F_l \) reaches choked flow at a smaller pressure differential.
