HW10 - ME 375 Out April 9 2009 Due HW#10 SPRING 2009...

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ME 375 HW #10 SPRING 2009 Out : April 9, 2009 Due : April 15, 2009 PROBLEM 1: (30%) A hydraulic lift used to raise automobiles for service is shown in the figure below. The hydraulic fluid entering the cylinder with flow rate Q exerts pressure P on the ram. The ram has cross- sectional area A and experiences viscous damping b with the walls of the cylinder. The combined mass of the ram and vehicle is given by m . (Note: ignore the fluid pressure variation in the cylinder due to gravity.) (a) Derive the differential equation that relates the vertical position y to fluid pressure P . (b) Write an expression for the fluid flow rate Q in terms of y and/or its derivatives. PROBLEM 2: (35%) The fluid system shown above represents the process of filling a remote tank or reservoir in a batch process at a chemical plant. Fluid provided by an ideal pressure source P s (gage pressure) is suddenly turned on or off by a rotary shut-off valve that offers very little resistance to flow when it is opened. The long line connecting the tank to the shut-off valve has an internal
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