## Problems Compressible Flow

1. A 12 in. ID gas pipeline carries methane (MW = 16) at a rate of 20,000 scfm. The gas enters the line at a pressure of 500psia, and a compressor station is located every 100 mi to boost the pressure back up to 500psia. The pipeline is isothermal at 70°F, and the compressors are adiabatic with an efficiency of 65%. What is the required horsepower for each compressor? Assume ideal gas.

2. Natural gas (CH4) is transported through a 6 in. ID pipeline at a rate of 10,000 scfm. The compressor stations are 150 mi apart, and the compressor suction pressure is to be maintained at 10 psig above that at which choked flow would occur in the pipeline. The compressors are each two stage, operate adiabatically with interstage cooling to 70°F, and have an efficiency of 60%. If the pipeline temperature is 70°F, calculate:

(a) The discharge pressure, interstage pressure, and compression ratio for the compressor stations.

(b) The horsepower required at each compressor station.

3. Natural gas (methane) is transported through a 20 in. sch 40 commercial steel pipeline at a rate of 30,000 scfm. The gas enters the line from a compressor at 100psi and 70°F. Identical compressor stations are located every 10mi along the line, and at each station the gas is recompressed to 100 psia and cooled to 70°F.

(a) Determine the suction pressure at each compressor station.

(b) Determine the horsepower required at each station if the compressors are 80% efficient.

(c) How far apart could the compressor stations be located before the flow in the pipeline becomes choked?

4. Natural gas (methane) is transported through an uninsulated 6 in. ID commercial steel pipeline, 1 mi long. The inlet pressure is 100 psi and the outlet pressure is 1 atm. What are the mass flow rate of the gas and the compressor power required to pump it? = 70°F, pgas = 0.02 cP.

5. It is desired to transfer natural gas (CH4) at a pressure of 200 psia and a flow rate of 1000 scfs through a 1 mi long uninsulated commercial steel pipeline into a storage tank at 20 psia. Can this be done using either a 6 in. or 12 in. ID pipe? What diameter pipe would you recommend? = 70°F, p = 0.02 cP.

6. A natural gas (methane) pipeline is to be designed to transport gas at a rate of 5000 scfm. The pipe is to be 6 in ID, and the maximum pressure that the compressors can develop is 1500 psig. The compressor stations are to be located in the pipeline at the point at which the pressure drops to 100 psi above that at which choked flow would occur (i.e., the suction pressure for the compressor stations). If the design temperature for the pipeline is 60°F, the compressors are

60% efficient, and the compressor stations each operate with three stages and interstage cooling to 60°F, determine

(a) The proper distance between compressor stations, in miles.

(b) The optimum interstage pressure and compression ratio for each compressor stage.

(c) The total horsepower required for each compressor station.

7. Ethylene leaves a compressor at 3500 psig and is carried in a 2 in, sch 40 pipeline, 100 ft long, to a unit where the pressure is 500 psig. The line contains two plug valves, one swing check valve, and eight flanged elbows. If the temperature is 100°F, what is the flow rate (inscfm)?

8. A 12 in. ID natural gas (methane) pipeline carries gas at a rate of 20,000 scfm. The compressor stations are 100 mi apart, and the discharge pressure of the compressors is 500psia. If the temperature of the surroundings is 70°F, what is the required horsepower of each compressor station, assuming 65% efficiency? If the pipeline breaks 10 mi downstream from a compressor station, what will be the flow rate through the break?

9. The pressure in a reactor fluctuates between 10 and 30 psig. It is necessary to feed air to the reactor at a constant rate of 20 lbm/hr, from an air supply at 100 psig, 70°F. To do this, you insert an orifice into the air line that will provide the required constant flow rate. What should the diameter of the orifice be?

10. Oxygen is to be fed to a reactor at a constant rate of 10 lbm/s from a storage tank in which the pressure is constant at 100 psig and the temperature is 70°F. The pressure in the reactor fluctuates between 2 and 10 psig, so you want to insert a choke in the line to maintain the flow rate constant. If the choke is a 2 ft length of tubing, what should the diameter of the tubing be?

11. Methane is to be fed to a reactor at a rate of 10 lbm/min. The methane is available in a pipeline at 20 psia, 70°F, but the pressure in the reactor fluctuates between 2 and 10 psia. To control the flow rate, you want to install an orifice plate that will choke the flow at the desired flow rate. What should the diameter of the orifice be?

12. Ethylene gas (MW - 28, k - 1.3, p - 0.1 cP) at 100°F is fed to a reaction vessel from a compressor through 100 ft of 2 in. sch 40 pipe containing two plug valves, one swing check valve, and eight flanged elbows. If the compressor discharge pressure is 3500 psig and the pressure in the vessel is 500 psig, what is the flow rate of the gas in scfm (1 atm, 60°F)?

13. Nitrogen is fed from a high pressure cylinder, through 1/4 in. ID stainless steel tubing, to an experimental unit. The line ruptures at a point 10 ft from the cylinder. If the pressure of the nitrogen in the cylinder is 3000 psig and the temperature is 70°F, what are the mass flow rate of the gas through the line and the pressure in the tubing at the point of the break?

14. A storage tank contains ethylene at 200 psig and 70°F. If a 1 in. line that is 6 ft long and has a globe valve on the end is attached to the tank, what would be the rate of leakage of the ethylene (in scfm) if

(a) The valve is fully open?

(b) The line breaks off right at the tank?

15. A 2 in. sch 40 pipeline is connected to a storage tank containing ethylene at 100 psig and 80°C.

(a) If the pipe breaks at a distance of 50 ft from the tank, determine the rate at which the ethylene will leak out of the pipe (in lbm/s). There is one globe valve in the line between the tank and the break.

(b) If the pipe breaks off right at the tank, what would the leak rate be?

16. Saturated steam at 200psig (388°F, 2.13ft3/lbm, p = 0.015cP) is fed from a header to a direct contact evaporator that operates at 10 psig. If the steam line is 2 in. sch. 40 pipe, 50 ft long, and includes four flanged elbows and one globe valve, what is the steam flow rate in lbm/hr?

17. Air is flowing from a tank at a pressure of 200psia and T = 70°F through a venturi meter into another tank at a pressure of 50 psia. The meter is mounted in a 6 in. ID pipe section (that is quite short) and has a throat diameter of 3 in. What is the mass flow rate of air?

18. A tank containing air at 100psia and 70°F is punctured with a hole 1/4in. in diameter. What is the mass flow rate of the air out of the tank?

19. A pressurized tank containing nitrogen at 800 psig is fitted with a globe valve, to which is attached a line with 10 ft of 1/4 in. ID stainless steel tubing and three standard elbows. The temperature of the system is 70°F. If the valve is left wide open, what is the flow rate of nitrogen, in lbm/s and also in scfm?

20. Gaseous chlorine (MW = 71) is transferred from a high pressure storage tank at 500psia and 60°F, through an insulated 2 in. sch 40 pipe 200 ft long, into another vessel where the pressure is 200 psia. What are the mass flow rate of the gas and its temperature at the point where it leaves the pipe?

21. A storage tank containing ethylene at a pressure of 200 psig and a temperature of 70°F springs a leak. If the hole through which the gas is leaking is 1/2 in. in diameter, what is the leakage rate of the ethylene, in scfm?

22. A high pressure cylinder containing N2 at 200 psig and 70°F is connected by 1/4 in. ID stainless steel tubing, 20 ft long to a reactor in which the pressure is 15 psig. A pressure regulator at the upstream end of the tubing is used to control the pressure, and hence the flow rate, of the N2 in the tubing.

(a) If the regulator controls the pressure entering the tubing at 25 psig what is the flow rate of the N2 (in scfm)?

(b) If the regulator fails so that the full cylinder pressure is applied at the tubing entrance, what will the flow rate of the N2 into the reactor be (in scfm)?

23. Oxygen is supplied to an astronaut through an umbilical hose that is 7 m long. The pressure in the oxygen tank is 200 kPa at a temperature of 10°C, and the pressure in the space suit is 20 kPa. If the umbilical hose has an equivalent roughness of 0.01mm, what should the hose diameter be to supply oxygen at a rate of 0.05 kg/s? If the suit springs a leak and the pressure drops to zero, at what rate will the oxygen escape?

24. Ethylene (MW = 28) is transported from a storage tank, at 250 psig and 70°F, to a compressor station where the suction pressure is 100 psig. The transfer line is 1 in. sch 80, 500 ft long, and contains two ball valves and eight threaded elbows. An orifice meter with a diameter of0.75 in. is installed near the entrance to the pipeline.

(a) What is the flow rate of the ethylene through the pipeline (in scfh)?

(b) If the pipeline breaks at a point 200 ft from the storage tank and there are 4 elbows and one valve in the line between the tank and the break, what is the flow rate of the ethylene (in scfh)?

(c) What is the differential pressure across the orifice for both cases (a) and (b), in inches of water?

25. Air passes from a large reservoir at 70°F through an isentropic converging-diverging nozzle into the atmosphere. The area of the throat is 1 cm2, and that of the exit is 2 cm2. What is the reservoir pressure at which the flow in the nozzle just reaches sonic velocity, and what are the mass flow rate and exit Mach number under these conditions?

26. Air is fed from a reservoir through a converging nozzle into a 1/2 in. ID drawn steel tube that is 15 ft long. The flow in the tube is adiabatic, and the reservoir temperature and pressure are 70°F and 100psia.

(a) What is the maximum flow rate (in lbm/s) that can be achieved in the tube?

(b) What is the maximum pressure at the tube exit at which this flow rate will be reached?

(c) What is the temperature at this point under these conditions?

27. A gas storage cylinder contains nitrogen at 250 psig and 70°F. Attached to the cylinder is a 3 in. long, 1/4 in. sch 40 stainless steel pipe nipple, and attached to that is a globe valve followed by a diaphragm valve. Attached to the diaphragm valve is a 1/4 in. (ID) copper tubing line. Determine the mass flow rate of nitrogen (in lbm/s) if

(a) The copper tubing breaks off at a distance of 30 ft downstream of the diaphragm valve.

(b) The pipe breaks off right at the cylinder.

28. A natural gas pipeline (primarily CH4) is supplied by a compressor. The compressor suction pressure is 20 psig, and the discharge pressure is 1000 psig. The pipe is 5 in. sch 40, and the ambient temperature is 80°F.

(a) If the pipeline breaks at a point 2 mi downstream from the compressor station, determine the rate at which the gas will escape (in scfm).

(b) If the compressor efficiency is 80%, what power is required to drive it?

29. You have to feed a gaseous reactant to a reactor at a constant rate of 1000 scfm. The gas is contained at 80°F and a pressure of 500 psigin a tank that is located 20 ft from the reactor, and the pressure in the reactor fluctuates between 10 and 20 psig. You know that if the flow is choked in the feed line to the reactor, then the flow rate will be independent of the pressure in the reactor, which is what you require. If the feed line has a roughness of 0.0018 in., what should its diameter be in order to satisfy your requirements? The gas has an MW of 35, an isentropic exponent of 1.25, and a viscosity of 0.01 cP at 80°F.

30. A pressure vessel containing nitrogen at 300°F has a relief valve installed on its top. The valve is set to open at a pressure of 125 psig and exhausts the contents to atmospheric pressure. The valve has a nozzle that is 1.5 in. in diameter and 4 in. long, which limits the flow through the valve when it opens.

(a) If the flow resistance in the piping between the tank and the valve, and from the valve discharge to the atmosphere are neglected, determine the mass flow through the valve when it opens in lbm/s.

(b) In reality, there is a 3 ft length of 3 in. pipe between the tank and the valve, and a 6 ft length of 4 in. pipe downstream of the valve discharge. What is the effect on the calculated flow rate of including this piping?

31. A storage tank contains ethylene at 80°F and has a relief valve that is set to open at a pressure of 250 psig. The valve must be sized to relieve the gas at a rate of 85 lbm/s when it opens. The valve has a discharge coefficient (the ratio of the actual to the theoretical mass flux) of 0.975.

(a) What should be the diameter of the nozzle in the valve, in inches? What horsepower would be required to compress the gas from 1 atm to the maximum tank pressure at a rate equal to the valve flow rate for:

(b) A single stage compressor;

(c) A two-stage compressor with intercooling. Assume 100% efficiency for the compressor.

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