A 25 mm radius piston is designed to fit inside a circular bore with a length of 75 mm. The fluid pressure on one end of the piston is 16 Mpa, while the fluid pressure on the opposite end of the piston is zero gauge pressure. The radial clearance between the piston and the bore is 10 microns, the fluid viscosity is 0.03 Pa-s, and the fluid density is 850 kg/ . Assuming that the eccentricity ratio is equal to 1.0 calculate the volumetric flow rate through the gap using the annular leak equation presented in Equation (2.81). Check the Reynolds number to verify that this is indeed a low Reynolds

A 25 mm radius piston is designed to fit inside a circular bore with a length of 75 mm. The fluid pressure on one end of the piston is 16 Mpa, while the fluid pressure on the opposite end of the piston is zero gauge pressure. The radial clearance between the piston and the bore is 10 microns, the fluid viscosity is 0.03 Pa-s, and the fluid density is 850 kg/ . Assuming that the eccentricity ratio is equal to 1.0 calculate the volumetric flow rate through the gap using the annular leak equation presented in Equation (2.81). Check the Reynolds number to verify that this is indeed a low Reynolds number flow. What is the volumetric flow rate and new Reynolds number when the eccentricity ratio is zero? Using Equation (2.81) the volumetric flow rate through the annular gap with an eccentricity ratio of 1 may be calculated as To verify that this is indeed a low Reynolds number flow Equation (2.51) may be used to show that Since the Reynolds number is much less than unity the flow is a low Reynolds number flow and the annular leakage equation used to calculate the volumetric flow rate is valid. If the eccentricity ratio goes to zero for a perfectly centered piston the volumetric flow rate and Reynolds number will decrease by a factor of 2/5. This means that the new volumetric flow rate is 0.0056 lpm and the new Reynolds number is 0.034.

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