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The University of Michigan
Department of Mechanical Engineering
ME 320 - Section 1
Exam II - Fall 2005
Problem 1
(20 points)
A highly viscous liquid of density
ρ
and viscosity
μ
slowly seeps up through the porous
ﬂoor of a rectangular channel which is open to the atmosphere above, as shown in
the ±gure. The porous area of the channel has a length
L
and width
b
and the liquid
±lters up with a uniform speed
V
through the porous area to form a liquid layer which
then moves horizontally from left to right with a velocity distribution
u
(
x, y
). The
channel is closed at the left end
x
= 0 and extends to the right beyond the end of
the porous section,
x
=
L
. The ﬂuid thickness
h
(
x
) decreases with increasing
x
,and
reaches a value of
H
at
x
=
L
.
In terms of the known parameters
p
atm.
,
g
,
ρ
,
μ
,
b
,
L
,
H
,
V
and the unknown layer
thickness
h
(
x
), derive expressions for:
(4 pnts) (a)
the volume ﬂow rate
Q
(
x
),
(2 pnts) (b)
the pressure distribution
p
(
x, y
), and
(8 pnts) (c)

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