Gases emerge from pipes differently than liquids because in addition to the exit velocity, resulting from pressure differential, gases gain significant volume when pressure is suddenly released, both proportionately, and due to compressibility factors. Several pioneers in the study of flow phenomena outlined various types of flow scenarios, including Daniel Bernoulli. Many of the formulas thus developed are in widespread use today, for calculating flows such as the discharge of gas from a pipe.
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Things you need
- Bernoulli Flow Equation
- SS Schedule 40 pipe data, two inch
Define the gas discharge application. In this example, a 100-foot long nominal two-inch Schedule 40S stainless steel pipe will be used to discharge gaseous nitrogen to atmosphere in the event of over pressure from a purge system. The system would normally contain nitrogen at 40 psig (pounds-per-square-inch-gauge) at standard ambient conditions of 14.696 psia atmospheric pressure and 15.6 degrees Celsius. A pressure relief valve, with a pressure regulating valve limiting the output to 6 psi, snaps open if the pressure reaches 60 psig and stays open until the pressure returns to 40 psig. With this information you can calculate the rate of gas discharge from the pipe when the flow starts and as it ends.
Consult flow data charts for Schedule 40S stainless steel pipe to ascertain pressure drop information. Since nitrogen comprises 78 per cent of air by volume, and the molecular weight is virtually that of air, at 28.014 compared to air at 28.9656, use flow data for air in Schedule 40 pipes which have the same size dimensions. The data for two-inch pipe with a 60 psi applied pressure and 5 per cent pressure loss (3 psi) through 100 feet of pipe shows a flow of 560 standard-cubic-feet-per-minute (SCFM). The flow corresponding to 40 psi applied pressure and 5 per cent pressure loss (2 psi) through 100 feet of pipe indicates 385 SCFM.
Adjust the flow value of 560 SCFM at the start of a discharge, assuming the greater the pressure drop through the pipe since the release valve regulates output to 6 psi. The discharge flow would therefore be 560 SCFM X (6 psi pressure loss/3 psi pressure loss)^0.5 = 1.414 X 560 = 792 SCFM.
Adjust the flow value of 385 SCFM for the 6-psi pressure loss over the 2-psi loss in the flow data. The discharge flow at the end of the discharge would be 385 X (6 psi loss/2 psi loss)^0.5 = 385 X 1.732 = 666.82 SCFM.
Tips and warnings
- Discharge gas flows should always be regulated to prevent supercritical supersonic flow and ear-splitting noise discharge.
- Use pipe sizes for emergency gas discharges well in excess of those necessary for laminar flow to prevent the possibility of over pressure and injury.
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