EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 8220100254963
Author: Palm
Publisher: MCG
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Chapter 12, Problem 12.3P
It is desired to control the angular displacement 9 of a space vehicle by controlling the applied torque T supplied by thrusters (Figure Pl2.3). The plant model is Design a compensator for this plant. The system must have a settling time no greater than 4 sec and a steady-state error of zero for a step command, and the dominant roots of the closed-loop system must have < > 0.45.
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A short brass cyclinder (denisty=8530 kg/m^3, cp=0.389 kJ/kgK, k=110 W/mK, and alpha=3.39*10^-5 m^2/s) of diameter 4 cm and height 20 cm is initially at uniform temperature of 150 degrees C. The cylinder is now placed in atmospheric air at 20 degrees C, where heat transfer takes place by convection with a heat transfer coefficent of 40 W/m^2K. Calculate (a) the center temp of the cylinder, (b) the center temp of the top surface of the cylinder, and (c) the total heat transfer from the cylinder 15 min after the start of the cooling. Solve this problem using the analytical one term approximation method. (Answer: (a) 45.7C, (b)45.3C, (c)87.2 kJ)
A short brass cyclinder (denisty=8530 kg/m^3, cp=0.389 kJ/kgK, k=110 W/mK, and alpha=3.39*10^-5 m^2/s) of diameter 4 cm and height 20 cm is initially at uniform temperature of 150 degrees C. The cylinder is now placed in atmospheric air at 20 degrees C, where heat transfer takes place by convection with a heat transfer coefficent of 40 W/m^2K. Calculate (a) the center temp of the cylinder, (b) the center temp of the top surface of the cylinder, and (c) the total heat transfer from the cylinder 15 min after the start of the cooling. Solve this problem using the analytical one term approximation method.
A 6 cm high rectangular ice block (k=2.22 W/mK, and alpha=0.124*10^-7 m^2/s) initially at -18 degrees C is placed on a table on its square base 4 cm by 4cm in size in a room at 18 degrees C. The heat transfer coefficent on the exposed surfaces of the ice block is 12 W/m^2K. Disregarding any heat transfer from the base to the table, determine how long it will be before the ice block starts melting. Where on the ice block will the first liquid droplets appear? Solve this problem using the analytical one-term approximation method.
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