Technician Eugene has observed that there is constant
leakage of oil from the piston-cylinder hydraulic system.
He wonders what is the flow rate of the leakage. The piston has a diameter
of 40 mm, and a length of 20 mm. The gap width between the piston
and cylinder is 0.008 mm. The working
fluid is SAE-30 oil. The pressure difference across the piston is 15
MPa.

Questions

Determine the velocity profile of the oil
in the gap between the piston and cylinder, and the leakage flow rate.

Dimensions of the Problem

Approach

Assume the piston is stationary.

The gap width is small, hence assume flow
between fixed parallel plates.

Assume the flow is steady, laminar and incompressible.

The viscosity and density of the SAE-30 oil are 0.38 N-s/m^{2} and 912 kg/m^{3}, respectively.

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