Leakage from the Piston-Cylinder System

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.

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

• 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/m² and 912 kg/m³, respectively.