An incompressible fluid with a density of 1008 kg/m^3 and a viscosity of 1.2 cP

Question

An incompressible fluid with a density of 1008 kg/m^3 and a viscosity of 1.2 cP is being pumped from Tank A to Tank B through a horizontal pipe with an internal diameter of 10 cm. The gas space above the liquid in Tank A (see figure) is vented to the atmosphere. The gas space above the liquid in Tank B is at a pressure of 5 atm. The mass flow rate through the 100 m long pipe is 6.048 kg/s. Assuming that the pipe is smooth and the tanks are very large and that there is no elevation difference in the levels of the fluid in the two tanks, calculate the required theoretical pump power. Explain what you are doing.

Explanation / Answer

First let us write down the known quantities,

Density = 1008 kg/m3

Pressure at A, PA = 1 atm = 101 kPa

Pressure at B, PB = 5 atm = 5 * 101 kPa = 505 kPa

Mass flow rate = 6.048 kg/s

1. The formula for the pump power is given by,

Power = Volumetric flow rate*Differential pressure (at the two tanks)

2. We have only the mass flow rate. But we also have the density

Volumetric flow rate = Mass flow rate/Density

= 6.048/1008

= 6e-3 m3/s

Differential Pressure = PB - PA = (505-101) kPa = 404 kPa

Substituting these into our formula for Power we get the required answer,

Power = Volumetric flow rate * Differential Pressure

= 6e-3 * 404kPa

= 2424 W or 2.424 kW

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