Pumping of fluids

The work done by the pump is found by setting up an energy balance equation. If W, is the shaft work done by unit mass of fluid on the surroundings, then —Ws is the shaft work done on the fluid by the pump. 

A three-stage compressor is required to compress air from 140 kN/m and 283 K to 4000 kN/m. Calculate the ideal intermediate pressures, the work required per kilogram of gas, and the isothermal efficiency of the process. It may be assumed that the compression is adiabatic and interstage cooling is provided to cool the air to the initial temperature. Show qualitatively, by means of temperature-entropy diagrams, the effect of unequal work distribution and imperfect intercooling, on the performance of the compressor. 

It is shown in Section 8.3.4 that the work done is a minimum when the intermediate pressures Pn and P,2 are related to the initial and hnal pressures Pi and P2 by  

A twin-cylinder, single-acting compressor, working at 5 Hz, delivers air at 515 kN/m at the rate of 0.2 m /s. If the diameter of the cylinder is 20 cm, the cylinder clearance ratio 5%, and the temperamre of the inlet air 283 K, calculate the length of stroke of the piston and the delivery temperature. 

A single-stage double-acting compressor running at 3 Hz is used to compress air from 110 kN/m and 282 K to 1150 kN/m. If the internal diameter of the cylinder is 20 cm, the length of stroke 25 cm, and the piston clearance 5%, calculate  

Methane is to be compressed from atmospheric pressure to 30 MN/m in four stages. Calculate the ideal intermediate pressures and the work required per kilogram of gas. Assume compression to be isentropic and the gas to behave as an ideal gas. Indicate on a temperature-entropy diagram the effect of imperfect intercooling on the work done at each stage. 

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The efficiency of the filtration process should not be significantly affected by the pressure differential across the surface of the membrane or pressure fluctuations produced by the pumping of fluids through it. 

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