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 Qexerts pressure Pon the ram. The ram has cross-sectional area Aand experiences viscous damping bwith 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 yto fluid pressure P. (b)Write an expression for the fluid flow rate Qin terms of yand/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 Ps(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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