Due:
In class, Friday
October 21, 2005
Name(s)
(up to three students per homework set)
:
1.
2.
3.
For instructor or TA use only:
Problem
Score
Points
1
15
2
10
3
15
4
15
5
15
6
15
7
15
ME 33
Fall Semester, 2005
Homework Set # 6
Professor J. M. Cimbala
Total:
100
1
.
(15 pts)
Consider a vertical rectangular flat plate of height
h
and width
w
exposed to stagnant water of depth
h
on one
side, and to atmospheric pressure on the other side as in Figure 324 in the text. Using centroids and centroidal moments of
inertia, it can easily be shown that the center of pressure is located at water depth 2
h
/3. Suppose you know nothing about
centroids, but instead approach this problem from the basic fundamentals only. In other words, suppose that all you know is
the hydrostatic pressure relation,
P
below
=
P
above
+
ρ
g
∆
z
. Integrate to prove that the center of pressure is located at water
depth 2
h
/3.
Hint
: Integrate to calculate the
actual
moment about the top of the plate, and set it equal to the moment
generated by the
resultant force
acting at the center of pressure. (You will also need to integrate to find the resultant force.)
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 Fall '05
 CIMBALA
 Force, Surface tension, Capillary action, Meniscus

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