There is a crack/leak/hole in the end of a closed pipe 50ft from the air tank. I am trying to determine the mass flow rate of the compressed air so I can know how quickly the tank will lose pressure. I don't know what formula I need to use, as well as what values I am missing that are necessary? Looking for an estimated value.
Assuming the following values:
Volume: 1350 ft3
Pressure: 170 psig
Exit Pressure: 0 psig
Tube Inner Diameter: 2 inches
Tube Length: 50 feet
molar mass air: 28.97 g/mol
Temperature is contant: 300K
Logan Tebbe Step 1 - Apply Bernoulli Equation at entry and exit point to find exit velocity. Step 2 - Measure the cross sectional area at exit point by given diameter.
Step 3 - Use the following relation with value of density of given fluid
"m = ρ*A*V (kg/s)"
You must know the diámeter of the hole at the closed end of the pipe. With this, and the pipe diámeter, calculate the flow rate of air as the flow through a restriction orifice. Use the following equation:
W = 1.25Cd**2Y(DP/ve)**0.5
W is the flow rate of air in Kg/h
C is the flow coefficient of the restriction orifice.
d is the hole diámeter in mm.
Y is the expansión factor of the air
DP is the differential pressure in Kg/cm**2
ve is the specific volume of the air
Sorry, I finalize my last answer.
The parameter ve is the specific volume of the air to the pressure of 170 psig.
Look for the parameters of Y and C for restriction orifices in Google.
Note that for the upstream pressure of 170 psig and the downstream pressure of 0 psig, the maximum DP may be more or less 150 psig.
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