ME 375
HOMEWORK #9
Fall 2010
Out:
October. 29
nd
, 2010
Due: November 5
th
, 2010
PROBLEM 1
:
(30%)
You have been asked to develop the differential equation that describes the following hydraulic system:
In this system, the pressure source
p
sr
is used to maintain the level of the tank.
You should treat the long pipe as
fluid inertance
I
.
There is a fluid resistance
R
1
to the left of the long pipe, and another fluid resistance
R
2
of the
valve to the right of the tank.
The fluid has density
ρ
and the entire system is subjected to gravity with
acceleration
g
.
(a)
Determine the differential equation that describes the height
h
in terms of the pressure source
p
sr.
(b)
Determine an expression for the steadystate height of the tank
h
ss
in terms of the pressure source flow
p
sr.
and the parameters defined above.
PROBLEM 2
:
(40%)
(a)
Problem 7.22 in Palm.
In particular, find the transfer function
)
(
)
(
2
s
Q
s
H
mi
.
(HINT: develop the equations for the gage pressures at the bottom of each tank, then convert these
pressures to the heights of the two tanks.
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 Fall '10
 Meckle
 Fluid Dynamics, Mass flow rate, Palm, Orifice plate, pressure source psr

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