# 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

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

$$L=\frac{9 \times P_1^2 \times D^5}{C^2}=\frac{9 \times P_2^2 \times D^5}{16 \times C^2}$$

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.)

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

### Material Properties

#### Properties:

Molecular Weight:

Ratio of Specific Heats:

Coefficient C:

Specific Gravity:

You may use table instead of calculator

What are the key factors that affect the performance of pressure relief valves?
The performance of pressure relief valves is affected by several key factors, including the valve’s set pressure, overpressure, and blowdown. The set pressure is the pressure at which the valve opens, while overpressure is the amount by which the system pressure exceeds the set pressure. Blowdown, on the other hand, is the difference between the set pressure and the pressure at which the valve reseats. Other factors that can impact performance include the valve’s flow coefficient, valve size, and the properties of the fluid being relieved.
How do I determine the required relief valve orifice area?

The required relief valve orifice area can be determined using the API 520/521 equations, which take into account the valve’s flow coefficient, the relieving pressure, and the required flow rate. The orifice area is typically calculated using the following equation: A = Q / (CKP), where A is the orifice area, Q is the required flow rate, C is the flow coefficient, K is the valve’s discharge coefficient, and P is the relieving pressure.

What is the significance of the relief valve vent line maximum length?

The relief valve vent line maximum length is critical because it affects the valve’s ability to relieve pressure safely and efficiently. A vent line that is too long can lead to excessive backpressure, which can prevent the valve from opening fully or cause it to reseat prematurely. The maximum length of the vent line can be calculated using the equation provided in the API 520/521 standards, which takes into account the valve’s set pressure, the vent line’s diameter, and the density of the fluid being relieved.

How do I select the correct relief valve for my application?

Selecting the correct relief valve for your application involves considering several factors, including the system’s design pressure, the relieving pressure, and the required flow rate. You should also consider the type of fluid being relieved, as well as any specific regulatory requirements or industry standards that apply. Other factors to consider include the valve’s material construction, its flow characteristic, and its certification or approval by relevant authorities.

What are the different types of pressure relief valves available?

There are several types of pressure relief valves available, including spring-loaded valves, pilot-operated valves, and rupture discs. Spring-loaded valves are the most common type and are suitable for most applications. Pilot-operated valves, on the other hand, are typically used for high-flow applications or where a high degree of accuracy is required. Rupture discs are used in applications where a rapid release of pressure is required, such as in fire suppression systems.

How do I ensure the proper installation and maintenance of pressure relief valves?

Proper installation and maintenance of pressure relief valves are critical to ensure their safe and efficient operation. Installation should be carried out in accordance with the manufacturer’s instructions and relevant industry standards. Regular maintenance should include inspections, testing, and cleaning of the valve to ensure it remains functional and free from blockages or corrosion.

What are the consequences of inadequate pressure relief valve sizing?

Inadequate pressure relief valve sizing can have serious consequences, including equipment damage, injury to personnel, and environmental harm. Undersized valves may not be able to relieve pressure quickly enough, leading to a buildup of pressure that can cause catastrophic failures. Oversized valves, on the other hand, can lead to excessive flow rates and energy losses. Proper sizing of pressure relief valves is therefore critical to ensure safe and efficient operation of process equipment.