Critical Pressure Ratios Water Liquids Control Valves

Overview

Engineering reference data for Critical Pressure Ratios Water Liquids Control Valves in process control.

Key Formulas

PID Controller

$u(t) = K_p e(t) + K_i \int e(t)dt + K_d \frac{de}{dt}$

Proportional-Integral-Derivative control.

Transfer Function

$G(s) = \frac{K}{\tau s + 1}$

First-order system.

Variables

Symbol	Description	Unit
$K_p$	Proportional gain	—
$K_i$	Integral gain	1/s
$K_d$	Derivative gain	s
$\tau$	Time constant	s

Critical Pressure Ratios in Control Valves

For control valve sizing, the critical pressure ratio ($R_c$) determines whether the flow through the valve is considered incompressible (sub-critical) or compressible (critical/choked). The following formulas define these ratios:

Critical Pressure Ratio for Water

The critical pressure ratio for water is typically a fixed value used to determine if cavitation or flashing will occur. $R_c = 0.96 - 0.28 \sqrt{\frac{P_v}{P_1}}$ where:

• $P_v$ is the vapor pressure of the liquid at inlet temperature.
• $P_1$ is the absolute inlet pressure.

Critical Pressure Ratio for Other Liquids

For hydrocarbons and other organic liquids, a simplified, conservative critical pressure ratio is often applied. $R_c = 0.9 - 0.1 \frac{P_v}{P_c}$ where:

• $P_c$ is the thermodynamic critical pressure of the specific liquid.

Engineering Note: These critical pressure ratios are key parameters in valve sizing equations (like the IEC 60534 standard). When the actual pressure drop ratio ($\Delta P / P_1$) exceeds $R_c$, the flow through the valve becomes choked, and further reduction in downstream pressure will not increase the flow rate. The sizing coefficient ($C_v$ or $K_v$) must then be calculated accordingly.

References

• Original Source