Control Valves

Overview

Engineering reference data for Control Valves in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Valve Fail-Safe Positions

Control valves are classified by their behavior when the control signal or air supply fails:

The choice of fail-safe position depends on process safety requirements—for example, a cooling water valve typically fails open (FO) to prevent overheating, while a fuel supply valve typically fails closed (FC) to prevent uncontrolled combustion.

Valve Authority

Valve authority is a dimensionless parameter that expresses the ratio of pressure drop across the control valve to the total pressure drop in the system:

$N = \frac{\Delta P_{\text{valve}}}{\Delta P_{\text{valve}} + \Delta P_{\text{system}}}$

Where:

• $N$ = valve authority (dimensionless, typically 0.3–0.7)
• $\Delta P_{\text{valve}}$ = pressure drop across the control valve at full open
• $\Delta P_{\text{system}}$ = pressure drop across all other system components

Higher authority ($N > 0.5$) provides better control but increases pumping costs. Lower authority reduces energy consumption but may result in poor controllability and nonlinear response.

Flow Characteristics

Control valve flow capacity vs. stem opening determines how the valve behaves through its travel range:

• Linear: Flow increases proportionally with valve opening—best for constant-pressure-drop systems
• Equal Percentage: Equal increments of stem travel produce equal percentage changes in flow—most common in process control where pressure drop varies with flow
• Quick Opening: Large flow increase near closed position—used for on/off or safety applications

The choice of characteristic should compensate for the system's pressure-flow relationship to achieve an overall linear installed response.

Cavitation

Cavitation occurs when local fluid pressure drops below the vapor pressure, forming vapor bubbles that collapse violently downstream. This causes noise, vibration, erosion, and reduced valve capacity. The cavitation index (or sigma) is used to predict and mitigate cavitation:

$\sigma = \frac{P_1 - P_v}{P_1 - P_2}$

Where $P_1$ is upstream pressure, $P_2$ is downstream pressure, and $P_v$ is vapor pressure. Multi-stage trim or backpressure increases are common mitigation strategies.

Seat Leakage Classifications

Control valve seat leakage is classified per ANSI/FCI 70-2 (equivalent to IEC 60534-4):

Related Tools

• Cv Calculator (Liquids): For sizing liquid control valves
• Cv Calculator (Gases): For sizing gas/vapor control valves
• Kv Sizing (Water): Metric-based water valve sizing
• Kv Sizing (Steam): Steam control valve design

References

• Original Source