PROBLEM 9.60*
The panel shown forms the end of a trough that is filled with water
to the line AA. Referring to section 9.2, determine the depth of the
point of application of the resultant of the hydrostatic forces acting
on the panel (the center of pressure).
PROBLEM 9.61
A vertical trapezoidal gate that is used as an automatic valve is held
shut by two springs attached to hinges located along edge AB.
Knowing that each spring exerts a couple of magnitude 1470 N · m,
determine the depth d of water for which the gate will open.
PROBLEM 9.61 (Continued)
PROBLEM 9.62
The cover for a 0.5-m-diameter access hole in a water storage
tank is attached to the tank with four equally spaced bolts as
shown. Determine the additional force on each bolt due to the
water pressure when the center of the cover is located 1.4 m
below the water surface.
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PROBLEM 9.63*
Determine the x coordinate of the centroid of the volume shown.
(Hint: The height y of the volume is proportional to the x coordinate;
consider an analogy between this height and the water pressure on a
submerged surface.)
PROBLEM 9.63* (Continued)
PROBLEM 9.64*
Determine the x coordinate of the centroid of the volume shown;
this volume was obtained by intersecting an elliptic cylinder with
an oblique plane. (Hint: The height y of the volume is
proportional to the x coordinate; consider an analogy between this
height and the water pressure on a submerged surface.)
PROBLEM 9.65*
Show that the system of hydrostatic forces acting on a
submerged plane area A can be reduced to a force P at the
centroid C of the area and two couples. The force P is
perpendicular to the area and is of magnitude Psin ,Ay
where
is the specific weight of the liquid, and the couples are
(sin)
xx
I
Mi
and (sin),
yxy
I
M
j
where
xy
I
xy dA
(see section 9.8). Note that the couples are
independent of the depth at which the area is submerged.
PROBLEM 9.65* (Continued)
PROBLEM 9.66*
Show that the resultant of the hydrostatic forces acting on a
submerged plane area A is a force P perpendicular to the area
and of magnitude Psin ,
A
ypA
where
is the specific
weight of the liquid and
p
is the pressure at the centroid C
of the area. Show that P is applied at a Point CP, called the
center of pressure, whose coordinates are /
Pxy
x
IAyand
/,
Px
yIAywhere xy
I
xydA (see section 9.8). Show also
that the difference of ordinates P
yy
is equal to 2/
x
ky
and
thus depends upon the depth at which the area is submerged.
P