How to Calculate Flow Based on Differential Pressure
Daniel Bernoulli first defined the relationships between pressure drop and stream velocity in flowing systems in the 1700s. Later, the Bernoulli Principle would lead developers in the area of flow measurements in straight streams such as in pipes. Today, much pressurerelated flow instrumentation finds its origin in this timeproven technology. You can use the same methodology to calculate flow based on differential pressure readings.
Water Flow Calculation

Define the liquid flow application. In this example, water flow is being monitored from a new deep well to determine its capacity. Pressure taps at either end of a 100foot section of 1inch ID (inner diameter) Schedule 40 PVC plastic pipe have been connected to a differential pressure indicator that reads out 96 inches H2O pressure drop when the well is flowing at peak capacity. With this information, you can calculate water flow rate through the pipe and the well's capacity.

Convert the 96inchesH2O differential pressure into poundspersquareinch (psi) differential pressure. Since each psi of head loss is equivalent to 27.71 inches of water column height, then 96 inches/27.72 inches = 3.464 psi differential pressure.

Consult the PVC Pipe Friction Loss Chart for 1inch diameter Schedule 40PVC plastic pipe. The reading for 25 gallons per minute (gpm) is 14.2 psi friction loss. Because the flow varies as a proportion of the square root of pressure difference, divide your 3.464 psi pressure drop by 14.2 psi pressure drop = 0.2439. Extracting the square root yields 0.4939 x 25gpm = 12.35 gpm flowing at the 3.464 psi differential pressure.

Verify the reasonableness of your calculation by crosschecking with an online calculator. The difference in flow rate is ((12.3512.22)/12.35 = 1 percent of flow, which is reasonable for flowing systems.
Air Flow Calculation

Define the air flow application. Schedule 40 steel pipe is often used to carry compressed air throughout industrial facilities. In this case, a 100foot length of 1inch Schedule 40 Steel Pipe has 40psi air flowing through it. If the pressure loss through the pipe is 1.6psi, you can calculate the air flow in standardcubicfeetperminute (SCFM).

Look up the air flow data in the chart for 1inch Schedule 40 steel pipe, which has a 1.05inch ID. Air at 40 psi losing 5 percent of its pressure or 40psi x 0.05 = 2.0 psi through 100 feet of pipe is flowing at a rate of 62SCFM.

Calculate the air flow for 40 psi air through the same system losing 1.6 psi to frictional losses, on the basis that flow of air at a given density (same pressure and temperature conditions) will vary proportionately as the square root of differential pressure decrease. Therefore, 1.6psi measured loss (differential pressure) / 2psi loss from the chart ) = 0.8. Extract the square root of 0.8 and multiply it by the flow rate with a 2psi differential. This yields 0.8944 x 62 = 55.45SCFM with a 1.6psi differential pressure reading.
References
Resources
Tips
 Manufacturers of pumps, valves, and piping systems have exhaustively tested and published data for their products, which makes flow calculations in given systems easy to calculate and crossvalidate.
Warnings
 Extreme caution should always be exercised when using any kind of plastic pipe for compressed air applications because of the possibility of flying fragments if the pipe should burst. Only certain products are rated for compressed air.
 Always wear protective eye wear when working with piping systems.
Writer Bio
Pauline Gill is a retired teacher with more than 25 years of experience teaching English to high school students. She holds a bachelor's degree in language arts and a Master of Education degree. Gill is also an awardwinning fiction author.
Photo Credits
 pvc image by Greg Pickens from Fotolia.com
 pressuregauge image by Dusan Radivojevic from Fotolia.com
 pipeline image by dinostock from Fotolia.com
 steel image by Oleg Guryanov from Fotolia.com
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