_ 1 _
ME 375
HOMEWORK #9
Spring 2011
Out:
Mar. 25
th
, 2011
Due:
Apr. 1
st
, 2011
Problem #1 (30%)
Consider the following system diagram, which represents a pump driven water flow source for a fire truck.
The
accumulator with capacitance C
f
is used to dampen the pressure and flow oscillations that occur when the end of
the fire hose is quickly opened or closed.
Flows Q
1
and Q
2
are volumetric flow rates.
Determine the input output differential equation with P
s
(t) as the input, and P
3r
= P
3
P
r
, as the output.
Known
constants are R
1
, R
2
, I, P
r
, and C
f
.
P
sr
(t)
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_ 2 _
Problem #2 (30%)
Consider the following system diagram, representing the process of filling a remote tank in a batch
process at a chemical plant.
a)
Assuming the shutoff valve is open.
Derive the inputoutput differential equation assuming that P
s
(t) is
the input, and P
3r
= P
3
P
r
, is the output.
Known constants are R
f
, I, A
t
, and P
r
.
Assume the density of the
fluid in the tank is
ρ
.
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 Fall '10
 Meckle
 Fluid Dynamics, Equations

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