Homework_1_solutions - CBE 162 Chemical Process Control...

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CBE 162: Chemical Process Control Homework 1 Solutions Question 1. (a) Description of control system (2 pts) (b) Statement of the control objective and description of the input (manipulated and disturbance), measured and unmeasured output variables (5 pts) (c) Block diagram illustrating process, inputs, outputs and control (3 pts) Question 2. (a) F i ( t ) = 10 liters/min F ( t ) = 10 + sin (0 . 1 t ) liters/min V (0) = 100 liters Writing mass balance, d ( V ρ ) dt = F i ρ i - F ( t ) ρ ( t ) Assumption: Density is constant throughout and independent of time, therefore cancels out. dV dt = F i - F ( t ) dV = ( F i - F ( t )) dt The integral form, based on initial conditions, is given by R V 100 dV 0 = R t 0 (10 - 10 - sin (0 . 1 t 0 )) dt 0 Integrating, V - 100 = 1 0 . 1 ( cos (0 . 1 t ) - 1) = 10( cos (0 . 1 t ) - 1) V = 90 + 10 cos (0 . 1 t ) Scoring break-up: 5 pts for mass balance and assumptions, 5 pts for integration and the plot. (b) Yes. The tank is filled to its steady state volume whenever the cosine function is maximum, i.e. when 0 . 1 t = 2 where n is an integer. The first instance is t = 62 . 8 mins when n = 1, and so on. (5 pts) 1
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Question 3. (a) The governing mass and heat balance equations are, respectively, dV dt = F i - F dT dt = F i V ( T i - T ) + Q ρC p V Equating the left hand side of each equation to zero at steady state and substituting the values given,
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