# How to Calculate the Reaction Thrust in a Relief Valve

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The reaction thrust on a valve is the force acting on it in the opposite direction of the fluid it expels. The fluid forces outward, and the thrust on the valve is the consequent reaction force. The thrust's size depends on momentum of the fluid, to which its temperature, specific heat capacity and molecular mass contribute. The thrust also depends on the fluid's static pressure, which derives from the dimensions of the valve and the pipe.

• Convert the fluid's temperature from degrees Fahrenheit to Rankine, an absolute scale, by adding 459.67. If, for instance, the fluid is at 120 degrees Fahrenheit: 120 + 459.67 = 579.67 degrees Rankine.

• Multiply the result by the ratio between the fluid's heat capacities at constant pressure and constant volume. When the ratio, for instance, equals 1.3: 579.67 x 1.3 = 753.6.

• Add 1 to the ratio from Step 2: 1.3 + 1 = 2.3.

• Multiply the result by the the fluid's molecular mass, measured in pounds per mole. If its molecular mass equals 40: 2.3 x 40 = 92.

• Divide the result from Step 2 by the result from Step 4: 753.6 / 92 = 8.19.

• Find the square root of your answer: 8.19 ^ 0.5 = 2.86.

• Multiply by the fluid's flow rate, in terms of pounds per hour. With a flow rate, for instance, of 15,000 pounds per hour: 2.86 x 15,000 = 42,900.

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• Divide by 366, a conversion constant: 42,900 / 366 = 117.2.

• Multiply the static pressure at the discharge point, measured in pounds per square inch, by the discharge area, measured in square inches. With a static pressure, for instance, of 16 pounds per square inch and a discharge area or 5 square inches: 16 x 5 = 80.

• Add the results from the previous two Steps: 117.2 + 80 = 197.2 pounds of reaction thrust.

## References

• "Ludwig's Applied Process Design for Chemical and Petrochemical Plants"; A. Kayode Coker; 2007
• "Lee's Loss Prevention in the Process Industries"; Sam Mannan; 2005
• Photo Credit valve image by askthegeek from Fotolia.com
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## Resources

• "CASTI Guidebook to ASME"; Glynn E. Woods, Roy B. Baguley; 2000

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