152 Chapter 4 / Mathematical Modeling of Fluid Systems and Thermal Systems
Since thermal resistance Rmay be written as
heat flow rate qmay be given, in terms of thermal resistance R,as
where is the bath temperature and is the thermometer temperature. Hence, we
can rewrite Equation (4–48) as
or
(4–49)
Equation (4–49) is a mathematical model of the thermometer system.
Referring to Equation (4–49), an electrical analog for the thermometer system can be writ-
ten as
An electrical circuit represented by this last equation is shown in Figure 4–41.
RC
deo
dt
+eo=ei
RC
du
dt
+u=ub
C
du
dt
=
ub-u
R
Q–+ub Q–+u
q=
AQ–+ubB-AQ–+uB
R
=
ub-u
R
R=
d(¢u)
dq
=
¢u
q
R
ei Ceo
Figure 4–41
Electrical analog of
the thermometer
system shown in
Figure 4–40.
Problems
B–4–1.Consider the conical water-tank system shown in
Figure 4–42. The flow through the valve is turbulent and is
related to the head Hby
whereQis the flow rate measured in m^3 sec and His in
meters.
Suppose that the head is 2 m at t=0. What will be the
head at t=60sec?
Q=0.005 1 H
2m
3m
2m
H
r
Figure 4–42Conical water-tank system.
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