Matlab Exam Questions And A+++++++++++ Answers!!!!

Exam 1  Page 1 of 4

SYSEN 533

Deterministic Modeling and Simulation

Exam 1

1. (25 pts) The compound tank system shown in Figure 1 consists of a spherical tank of radius R1 and a 

cylindrical tank of diameter D2. A liquid of constant density is fed at a volumetric rate F1in

into the 

top of a spherical tank and volumetric rate F2in into the top of the cylindrical tank. The spherical and 

cylindrical tanks interact through the pipe connecting them. The flow rates into the connecting pipe 

depend on the heights of the liquid in the tanks. The volumetric flow rate out of the spherical tank 

into the pipe is given by

1out 1 1

F kh = , while the volumetric flow rate out of the cylindrical tank into 

the pipe is given by 

2out 1 2

F kh = where h1 and h2 are the heights of the liquid in the spherical and 

cylindrical tanks respectively and 

1

k is the common valve coefficient. The cylindrical tank also has a 

drain on the right-hand side which has volumetric flow rate

3out 2 2

F kh =  where 

2

kis the valve 

coefficient for the right-hand side drain.

a)  Obtain a dynamic model that describes the heights of the liquid in the tanks. Is this a linear or 

nonlinear model?

b)  For constant input flow rates, F1in

and F2in, analytically determine the steady-state values of h1 and 

h2. Do the shapes and dimensions of the tanks affect the steady-state values?

Note that you do not need to solve the differential equations for the steady state analysis.

c)  Simulate the system and plot the heights of the liquid in the tanks versus time for constant input 

flow rates using the values given in the table below. (Run the simulation for 2000 sec)

F1in 2.0 ft

3

/s  F2in    1.0 ft

3

/s

R1  10.0 ft  D2  20.0 ft

k1 2.0 ft

5/2

/s  k2    3.0 ft

5/2

/s

h1(0)    4.0 ft  h2(0)    4.0 ft

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