##### (Solution)-An 8 inch diameter casing (impermeable metal pipe) extends

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**Question**

1. Consider the following structure: An 8 inch diameter casing (impermeable metal pipe) extends 7000 feet into the ground. The casing is empty and clear of obstruction except for the last 2 feet which contains a permeable plug (k=100 mD). Outside the plug (point A) is an essentially inexhaustible source of ideal gas at 200 atmospheres pressure and 125 degrees celsius. The top of the casing has a regulator that feeds the gas into a processing pipe line at 5 atmospheres and 25 degrees celsius. The flow rate of this is 0.02 cp ideal gas into the 5 atmosphere pipe line (point C) is 10,000 cm^3/sec. Point A: Pressure is 200 atm and temperature is 125 degrees celsiusPoint B: Pressure is 10 atm and temperature is 115 degrees celsiusPoint C: Pressure is 5 atm and temperature is 25 degrees celsius a. Remembering that 1 inch=2.54 cm. What is the volume flow rate into the plug at point A? b. What is the volume flow rate leavingthe plug at point B? 2. Consider the following pipe assembly containing two permeable filters each of length L seperated by an equal distance. The cross sectional areas are A, and the filters have permeabilities k1 and k2. An incompressible fluid of viscosity u flows through this system at a volume flow rate of Q. The input pressure is P_i, the output pressure is P_o and the pressure between the filters is P_m. a. Derive an expression relating k1, k2, and the three pressures P_i, P_o, and P_m. b. If P_i=10 atmospheres, P_m= 3 atmospheres, P_o= 1 atmosphere, and k2= 700mD, what is the value of k1? c. If in addition you are told the fluid viscosity is 7 cp, the length L=20 cm, and the area A is 40 cm^2 what is the volume flow rate?

Solution ID:10086441 | Question answered on 16-Oct-2016

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