Question

9.25. A pumping station consists of a pump, a long pipe, and a tank with an outflow valve as shown in Fig. 9.44. The goal is to design the system so that there will be no overshoot in the depth of fluid in the storage tank resulting from transient changes in the pump pressure Pp) Tank Valve Long pipeI atm Pump Fluid reservoir Figure 9.44: A fluid pumping statio (a) Assume the pipe resistance can be neglected and that the pump may be modeled as a pressure source. Formulate a system model and derive the state equations. Develop a single differential equation relating the pressure at the bottom of the tank to the pump pressure, and determine the system undamped natural frequency and damping ratio. (b) 330 First- and Second-Order System Response Chap. 9 (c) A test is conducted on the system, in which the pump is suddenly energized to provide a pressure Pp(r)-Po. If the outflow valve is shut, that is R-oo, determine and sketch the tank pressure response. In the test it is observed that the peak values of pressure occur every 0.4 s. What is the system undamped natural frequency? (d) The goal is to fill the tank without a water spill caused by overshoot in the response. If the tank area A = 20 m2, what is the maximum value of valve resistance R that may be selected to prevent overshoot?

Answer 1

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