dsc_hw_3_w09 - Homework Set #3: MAE 3600 Dynamic Systems...

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Homework Set #3: MAE 3600 – Dynamic Systems and Control, Winter 2009 Due date: Friday, February 25, 2009 Problem 1 . A liquid-level system is shown below. The input water mass-flow rate is in w . The tank has constant cross-sectional area A . Mass-flow rate out of the tank is w out , which is modeled as flow through a small orifice with constant area a 0 and discharge coefficient C d (i.e., turbulent flow). a) Derive the system model with absolute pressure p (at the bottom of the tank) as the dynamic variable. b) Derive the system model with liquid height h as the dynamic variable. Problem 2 . The oven shown below has a heating element which has its own thermal capacitance C 2 , due to its mass. The oven air has thermal capacitance C 1 . The heater has temperature θ 2 , the oven air has temperature 1 , and the outside temperature is a . The oven has insulation R 1 , and the thermal resistance of the heater-air interface is R 2 . The heat flow rate delivered to the heater mass is
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This note was uploaded on 06/29/2011 for the course MAE 3600 taught by Professor Pai during the Spring '09 term at Missouri (Mizzou).

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dsc_hw_3_w09 - Homework Set #3: MAE 3600 Dynamic Systems...

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