Safety Valves Liquids Pilot

Overview

Engineering reference data for Safety Valves Liquids Pilot 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

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Minimum Discharge Area for Pilot Operated Relief Valves

The minimum discharge area $A$ of a pilot operated relief safety valve in a liquid system can be calculated using the following formula:

$$A = \frac{q \cdot SG^{1/2}}{36.81 \cdot K_{visc} \cdot dp^{1/2}}$$

where:

• $A$ is the discharge area in square inches (in²),
• $q$ is the relieving capacity in gallons per minute (GPM),
• $SG$ is the specific gravity of the fluid (dimensionless),
• $K_{visc}$ is the viscosity correction factor (typically 1.0 for most water systems),
• $dp$ is the differential pressure in pounds per square inch gauge (psig), computed as set pressure + over pressure - back pressure.

This formula accounts for fluid properties and system pressures to ensure proper valve sizing for safe relief in liquid applications. Always verify units consistency and consider applicable standards.

References

• Original Source