Homework Set #3:
MAE 3600 – Dynamic Systems and Control, Winter 2009
Due date: Friday, February 25, 2009
Problem 1
.
A liquidlevel system is shown below.
The input water massflow rate is
in
w
.
The tank has constant crosssectional area
A
.
Massflow 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 heaterair interface is
R
2
.
The
heat flow rate delivered to the heater mass is
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 Spring '09
 Pai
 Fluid Dynamics, Thermodynamics, Heat, DYNAMIC SYSTEMS, conical water tank, Oven air C1

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