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me375_fa10_hwk09

# me375_fa10_hwk09 - ME 375 HOMEWORK#9 Out October 29nd 2010...

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ME 375 HOMEWORK #9 Fall 2010 Out: October. 29 nd , 2010 Due: November 5 th , 2010 PROBLEM 1 : (30%) You have been asked to develop the differential equation that describes the following hydraulic system: In this system, the pressure source p sr is used to maintain the level of the tank. You should treat the long pipe as fluid inertance I . There is a fluid resistance R 1 to the left of the long pipe, and another fluid resistance R 2 of the valve to the right of the tank. The fluid has density ρ and the entire system is subjected to gravity with acceleration g . (a) Determine the differential equation that describes the height h in terms of the pressure source p sr. (b) Determine an expression for the steady-state height of the tank h ss in terms of the pressure source flow p sr. and the parameters defined above. PROBLEM 2 : (40%) (a) Problem 7.22 in Palm. In particular, find the transfer function ) ( ) ( 2 s Q s H mi . (HINT: develop the equations for the gage pressures at the bottom of each tank, then convert these pressures to the heights of the two tanks.

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