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# Homework Set No. 5 1. CBE 150A Spring 2014 R. B. Eldridge An emergency vent line from a reactor is 55 feet long and has an inside diameter of 4.026

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Homework Set No. 5 CBE 150A Spring 2014 R. B. Eldridge 1. An emergency vent line from a reactor is 55 feet long and has an inside diameter of 4.026 inches. The surface roughness of the pipe is 0.0012 inches. The line discharges hydrogen to the atmosphere (P = 14.7 psia) a) If the mass flow rate of hydrogen is 95 lb / minute and the temperature is 100 F, what is the pressure within the vessel ? Assume the gas flow is isothermal. b) Could a mass flow rate of 100 lb/minute be attained in this emergency vent line with this vessel pressure ?? Data for hydrogen: = 0.014 cP C p = 3.5 BTU/lb F = 1.4 Z = 1.00 2. Air flows from a large supply tank in which the pressure is 147 psig and the temperature is 160 F through a converging - diverging nozzle. The velocity at the throat of the nozzle is sonic. A normal shock occurs at a point in the diverging section of the nozzle where the cross-sectional area is 1.44 times the cross-sectional area of the throat. a) Compute the Mach number, pressure, and temperature just upstream of the shock. b) Compute the Mach number, pressure, and temperature just downstream of the shock. 3. Natural gas (primarily methane) is being transferred through a buried pipeline in southeast California. 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 Buba’s back-hoe digs a hole in the line at a point 2 miles downstream of the compressor station, determine the rate at which the gas escapes in SCFM (60 F and 1 atm) b) If the compressor efficiency is 80 % what power is required to drive it ? 4. A compressor / pipeline system is being designed for an offshore platform. The system will compress and transport natural gas (primarily methane) from a suction pressure of 350 psia at 60 F. The platform is located 100 miles off-shore. The gas must arrive on shore at a pressure of 1000 psi. The platform produces 2.0 billion standard cubic feet per day (standard conditions = 60 F and 1 atm). The pipeline is 48 inches in diameter with an roughness factor (k/D) of 0.0004. The sea bed is a constant 60 F. Maximum compressor discharge temperature is limited to 350 F. The compressor efficiency is 75 percent (related to reversible compression). The natural gas viscosity is 0.01 cP at 60 F. Find: a) The required compressor discharge pressure b) The required number of compression stages. c) The compressor horsepower.

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