# Relief Valve Calculations And Equations

Pressure relief devices (PRD’s) are widely and effectively used to protect process equipment such as piping systems, pressure vessels, distillation columns and other equipment from pressures exceeding the design-pressure rating by more than a fixed predetermined amount. The aim of pressure relief valves is to prevent damage to equipment, prevent injury to personnel and to avoid potential risks to the environment.

## Relief Valve Vent Line Maximum Length

P1 = 0.25 × [(PRESSURE SETTING × 1.1) + 14.7]

P2 = [(PRESSURE SETTING × 1.1) + 14.7]

L = Maximum Length of Relief Vent Line (Feet)

D = Inside Diameter of Pipe (Inches)

C = Minimum Discharge of Air (Lbs./Min.)

## Relief Valve Sizing

### Relief Valve Equation Definitions:

A = Minimum Required Effective Relief Valve Discharge Area (Square Inches)

GPM = Required Relieving Capacity at Flow Conditions (Gallons per Minute)

W = Required Relieving Capacity at Flow Conditions (Lbs./Hr.)

SCFM = Required Relieving Capacity at Flow Conditions (Standard Cubic Feet per Minute)

G = Specific Gravity of Liquid, Gas, or Vapor at Flow Conditions
Water = 1.0 for most HVAC Applications
Air = 1.0

C = Coefficient Determined from Expression of Ratio of Specific Heats
C = 315 if Value is Unknown

K = Effective Coefficient of Discharge
K = 0.975

KB = Capacity Correction Factor Due to Back Pressure
KB = 1.0 for Atmospheric Discharge Systems

KV = Flow Correction Factor Due to Viscosity
KV = 0.9 to 1.0 for most HVAC Applications with Water

KN = Capacity Correction Factor for Dry Saturated Steam at Set Pressures above 1500 Psia and up to 3200 Psia
KN = 1.0 for most HVAC Applications

KSH = Capacity Correction Factor Due to the Degree of Superheat
KSH = 1.0 for Saturated Steam

Z = Compressibility Factor
Z = 1.0 If Value is Unknown

P = Relieving Pressure (Psia)
P = Set Pressure (Psig) + Over Pressure (10% Psig) + Atmospheric Pressure (14.7 Psia)

∆P = Differential Pressure (Psig)
∆P = Set Pressure (Psig) + Over Pressure (10% Psig) − Back Pressure (Psig)

T = Absolute Temperature (°R = °F. + 460)

M = Molecular Weight of the Gas or Vapor

### Relief Valve Sizing Notes

• When multiple relief valves are used, one valve shall be set at or below the maximum allowable working pressure, and the remaining valves may be set up to 5 percent over the maximum allowable working pressure.
• When sizing multiple relief valves, the total area required is calculated on an overpressure of 16 percent or 4 Psi, whichever is greater.
• For superheated steam, the correction factor values listed below may be used: