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.

**Contents**hide

## Relief Valve Vent Line Maximum Length

The equation for the maximum length of a relief vent line is:

P_{1} = 0.25 × [(PRESSURE SETTING × 1.1) + 14.7]

P_{2} = [(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.)

The first term in the equation, \(\frac{9 \times P_1^2 \times D^5}{C^2}\), represents the pressure drop in the relief vent line due to friction. The second term in the equation, \(\frac{9 \times P_2^2 \times D^5}{16 \times C^2}\), represents the pressure drop in the relief vent line due to the expansion of the gas as it flows through the pipe.

The equation is set equal to zero because it represents the maximum length of the relief vent line for which the pressure drop will not exceed the set pressure of the relief valve. If the length of the relief vent line is greater than the maximum length, then the pressure drop in the line will exceed the set pressure of the relief valve, and the valve will not open properly.

The equation can be used to design relief vent lines for a variety of applications, such as pressure vessels, boilers, and compressors. It is important to note that the equation is only valid for single-phase gas flow. If the fluid flowing through the relief vent line is a two-phase mixture of gas and liquid, then the equation will need to be modified.

Here is an example of how to use the equation to calculate the maximum length of a relief vent line:

The first step is to calculate the back pressure at the relief valve outlet:

`P_1 = 0.25 * [(150 psig + 14.7 psia) * 1.1] + 14.7 psia = 42.6 psia`

The next step is to calculate the inside diameter of the relief vent pipe:

`D = 1.5 inches - 0.133 inches (wall thickness of Schedule 40 steel pipe) = 1.367 inches`

Finally, we can substitute all of the known values into the equation to calculate the maximum length of the relief vent line:

`L = 9 * 42.6^2 * 1.367^5 / 100^2 = 272 feet`

Therefore, the maximum length of the relief vent line is 272 feet.

## Relief Valve Sizing

### Liquid System Relief Valves and Spring Style Relief Valves:

$$ A=\frac{G P M \times \sqrt{G}}{28.14 \times K_B \times K_V \times \sqrt{\Delta P}} $$### Liquid System Relief Valves and Pilot Operated Relief Valves:

$$ A=\frac{G P M \times \sqrt{G}}{36.81 \times K_V \times \sqrt{\Delta P}} $$### Steam System Relief Valves:

$$ A=\frac{W}{51.5 \times K \times P \times K_{S H} \times K_N \times K_B} $$### Gas and Vapor System Relief Valves (Lb./Hr.):

$$ A=\frac{W \times \sqrt{T Z}}{C \times K \times P \times K_B \times \sqrt{M}} $$### Gas and Vapor System Relief Valves (SCFM):

$$ A=\frac{S C F M \times \sqrt{T G Z}}{1.175 \times C \times K \times P \times K_B} $$**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 (pounds per hour)**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 the expression of the 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) + overpressure (10% psig) + atmospheric pressure (14.7 psia))**∆P:**Differential pressure (psig) (∆P = set pressure (psig) + overpressure (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:

### Superheat Calculator

Selected Superheat: 0 °F

Correction Factor: 0.97

Superheat Value | Correction Factor |

Superheat up to 400 °F | 0.97 (Range 0.979–0.998) |

Superheat up to 450 °F | 0.95 (Range 0.957–0.977) |

Superheat up to 500 °F | 0.93 (Range 0.930–0.968) |

Superheat up to 550 °F | 0.90 (Range 0.905–0.974) |

Superheat up to 600 °F | 0.88 (Range 0.882–0.993) |

Superheat up to 650 °F | 0.86 (Range 0.861–0.988) |

Superheat up to 700 °F | 0.84 (Range 0.841–0.963) |

Superheat up to 750 °F | 0.82 (Range 0.823–0.903) |

Superheat up to 800 °F | 0.80 (Range 0.805–0.863) |

Superheat up to 850 °F | 0.78 (Range 0.786–0.836) |

Superheat up to 900 °F | 0.75 (Range 0.753–0.813) |

Superheat up to 950 °F | 0.72 (Range 0.726–0.792) |

Superheat up to 1000 °F | 0.70 (Range 0.704–0.774) |

### Material Properties

#### Properties:

**Molecular Weight:**

**Ratio of Specific Heats:**

**Coefficient C:**

**Specific Gravity:**

You may use table instead of calculator

GAS OR VAPOR | MOLECULAR WEIGHT | RATIO OF SPECIFIC HEATS | COEFFICIENT C | SPECIFIC GRAVITY |

Acetylene | 26.04 | 1.25 | 342 | 0.899 |

Air | 28.97 | 1.40 | 356 | 1.000 |

Ammonia (R-717) | 17.03 | 1.30 | 347 | 0.588 |

Argon | 39.94 | 1.66 | 377 | 1.379 |

Benzene | 78.11 | 1.12 | 329 | 2.696 |

N-Butane | 58.12 | 1.18 | 335 | 2.006 |

Iso-Butane | 58.12 | 1.19 | 336 | 2.006 |

Carbon Dioxide | 44.01 | 1.29 | 346 | 1.519 |

Carbon Disulphide | 76.13 | 1.21 | 338 | 2.628 |

Carbon Monoxide | 28.01 | 1.40 | 356 | 0.967 |

Chlorine | 70.90 | 1.35 | 352 | 2.447 |

Cyclohexane | 84.16 | 1.08 | 325 | 2.905 |

Ethane | 30.07 | 1.19 | 336 | 1.038 |

Ethyl Alcohol | 46.07 | 1.13 | 330 | 1.590 |

Ethyl Chloride | 64.52 | 1.19 | 336 | 2.227 |

Ethylene | 28.03 | 1.24 | 341 | 0.968 |

Helium | 4.02 | 1.66 | 377 | 0.139 |

N-Heptane | 100.20 | 1.05 | 321 | 3.459 |

Hexane | 86.17 | 1.06 | 322 | 2.974 |

Hydrochloric Acid | 36.47 | 1.41 | 357 | 1.259 |

Hydrogen | 2.02 | 1.41 | 357 | 0.070 |

Hydrogen Chloride | 36.47 | 1.41 | 357 | 1.259 |

Hydrogen Sulphide | 34.08 | 1.32 | 349 | 1.176 |

Methane | 16.04 | 1.31 | 348 | 0.554 |

Methyl Alcohol | 32.04 | 1.20 | 337 | 1.106 |

Methyl Butane | 72.15 | 1.08 | 325 | 2.491 |

Methyl Chloride | 50.49 | 1.20 | 337 | 1.743 |

Natural Gas | 19.00 | 1.27 | 344 | 0.656 |

Nitric Oxide | 30.00 | 1.40 | 356 | 1.036 |

Nitrogen | 28.02 | 1.40 | 356 | 0.967 |

Nitrous Oxide | 44.02 | 1.31 | 348 | 1.520 |

N-Octane | 114.22 | 1.05 | 321 | 3.943 |

Oxygen | 32.00 | 1.40 | 356 | 1.105 |

N-Pentane | 72.15 | 1.08 | 325 | 2.491 |

Iso-Pentane | 72.15 | 1.08 | 325 | 2.491 |

Propane | 44.09 | 1.13 | 330 | 1.522 |

R-11 | 137.37 | 1.14 | 331 | 4.742 |

R-12 | 120.92 | 1.14 | 331 | 4.174 |

R-22 | 86.48 | 1.18 | 335 | 2.985 |

R-114 | 170.93 | 1.09 | 326 | 5.900 |

R-123 | 152.93 | 1.10 | 327 | 5.279 |

R-134a | 102.03 | 1.20 | 337 | 3.522 |

Sulfur Dioxide | 64.04 | 1.27 | 344 | 2.211 |

Toluene | 92.13 | 1.09 | 326 | 3.180 |