# How to Determine Differential Pressure to Flow Rate

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Flows of liquids, gases and even particulate solids occur as varying pressures act upon masses of materials. In weather, higher pressure on one side of a weather system will push it towards an area of lower pressure. In pipelines, ducts and conduits, higher pressure will always push liquid or gaseous materials towards an area with lower pressure. Differential pressure, or the net difference between these higher and lower pressures, can be determined from specified flow rates within defined flowing systems as well as its opposite with a calculator and published flow data.

### Things You'll Need

• Calculator
• Flow data for specific pipe system

## Determining Differential Pressure from Flow Rate

• Define the flowing system. In this example, water is flowing from a reservoir by gravity down a hill and into a holding tank through a 536-foot length of smooth 6-inch Schedule 40-Steel pipe. If you know that the flow through the pipe is 1,311 gallons per minute, or gpm, you can calculate the differential pressure across the pipe's length and therefore the reservoir's elevation above the tank.

• Look up the differential pressure versus flow data for nominal 6-inch Schedule 40-steel pipe. Note that the flow data for 1,427 gpm is 5.7 pounds per square inch, or psi, per 100 feet of this pipe.

• Calculate the actual differential pressure per 100 feet of pipe based on this data. Since flow varies as the square root of differential pressure changes, then the 1,311-gpm flow is a result of the square of (1311/1427) or (0.9187)^2 = 0.844. Multiplying 0.844 times the 5.7-psi differential pressure per 100 feet of this pipe yields a 4.81-psi differential pressure per 100 feet of pipe.

• Calculate the differential pressure over the entire 536 feet of pipe, and the elevation difference causing the pressure differential. Multiply 4.81 psi/100 feet by 536 feet of pipe to yield a total of 25.78-psi differential pressure. Since each 2.31 feet of water elevation results in 1 psi of static pressure head, then the reservoir is 25.78 * 2.31 = 59.55 feet higher than the tank, which would certainly result in this high flow rate without a pump.

## Calculate Flow Rate from Differential Pressure

• Define the flowing system. Compressed air at a pressure of 100 psi is flowing through a 100-foot section of nominal 1-inch Schedule 40-steel pipe. If you know that the total pressure loss, or differential pressure, is 4 psi, you can calculate the air flow rate in standard cubic feet per minute, or SCFM.

• Look up the flow data for 100-psi compressed air for 1-inch Schedule 40-steel pipe. For 100-psi air with a 5-percent loss, or 5-psi, there is a flow of 150 SCFM.

• Calculate the actual air flow based on a 4-psi differential pressure versus a 5-psi differential pressure. Flow varies as the square root of pressure differential, so multiplying 150 SCFM by square root(4 psi/5 psi) = 150 * 0.8944 = 134.16 SCFM.

## Tips & Warnings

• Take advantage of elevation if it exists to ease pumping requirements wherever possible by increasing pipe size.
• Never convey compressed air through Schedule 40 PVC plastic pipes as they may shatter upon overpressure or impact and send fragments through the air as dangerous projectiles.

## References

• Photo Credit steel image by Oleg Guryanov from Fotolia.com Steam Pipes image by Andrei Merkulov from Fotolia.com gauge image by DXfoto.com from Fotolia.com
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