The flow of liquids, vapours and gases from an area of higher pressure to an area of lower pressure can be compared to a vehicle rolling downhill from a higher to a lower elevation. The volumetric or linear velocity flow through a pipe or conduit of known cross sectional area is an expression of kinetic energy while the differential pressure is an expression of net potential energy that is converted to kinetic energy in the pipe. The Darcy-Weisbach Flow Equation determines that flow rate varies proportionately to the square root of differential pressure changes.
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Things you need
- Flow -- Pressure Data Chart for Schedule 40 PVC Plastic Pipe
Define the flow to differential pressure application. In this example, a 2-inch Schedule 40 PVC plastic pipe will be used to carry water from a runoff catch basin on the side of a hill to a holding tank in a field for irrigation purposes in a third-world country. There is a manual ball type shut-off valve in the pipe on top of the tank that presents no restriction to flow when it is fully open. If you know that the pipe is 1,200 feet long, and that the elevation of the catch basin water level is 170 feet higher than the shut-off valve, then you can calculate the flow rate through the 2-inch pipe from differential pressure.
Determine the pressure created at the bottom of the pipe due to elevation pressure with the valve closed and no flow. Since each 2.31 feet of elevation results in one pound per square inch of pressure, then the pressure in the pipe would be 170 feet elevation/2.31 feet elevation/psi = 73.59 psi right before the closed valve.
Calculate the pressure drop in psi per 100 feet of pipe to utilise the flow data charts which present pressure loss per 100 feet of pipe. Dividing the 73.59 psi static pressure by 1,200 feet /100 feet yields a differential pressure of 73.59/12 = 6.13 psi per 100 feet.
Consult the Schedule 40 PVC Pipe Flow Chart for the flow versus pressure correlations for 2-inch pipe. The chart shows a 6.5 psi loss for a 100-gallon-per-minute flow rate, which is close to the example application.
Adjust the flow data from the chart for the exact 6.13-psi differential pressure (pressure loss) per 100 feet of pipe in your application. Plugging your values into the square root formula, Flow = (6.13 psi/6.5-psi)^0.5 X 100 gpm = 0.971 X 100 = 97.1 gallons per minute when the ball valve is fully open and doesn't restrict the flow.
Tips and warnings
- Use less costly smaller diameter pipes and smaller valves to regulate flow to lower rates if the higher rates allowed by larger more costly materials will never be required.
- Never shut off a water flow valve quickly, as the momentum of a large amount of water under pressure ending suddenly can burst the pipe or pull it out of its mountings, causing damage to the pipe as a minimum and injury in worse cases.
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