The plane region A is submerged in a fluid of weight density γ . The resultant force of the fluid pressure on the region is R acting at the point C (called the pressure center) located at the distance h below the surface of the fluid. Show that R = γ Q a and h = I a / Q a , where Q a and I a are the first and second moments of A about the axis a - a .
The plane region A is submerged in a fluid of weight density γ . The resultant force of the fluid pressure on the region is R acting at the point C (called the pressure center) located at the distance h below the surface of the fluid. Show that R = γ Q a and h = I a / Q a , where Q a and I a are the first and second moments of A about the axis a - a .
Solution Summary: The author explains that R=gamma Q_a and h=
The plane region A is submerged in a fluid of weight density
γ
.
The resultant force of the fluid pressure on the region is R acting at the point C (called the pressure center) located at the distance h below the surface of the fluid. Show that
R
=
γ
Q
a
and
h
=
I
a
/
Q
a
,
where
Q
a
and
I
a
are the first and second moments of A about the axis a-a.
Find the force on the parabolic plate if it is partly submerged in a liquid weighing 48
Ib/ft³ so that its axis is parallel to and 3 ft below the surface of the liquid. The figure is
shown below.
P(x, y)-
Ay
(4,6)
3-y
(4,-6)
Surface of Liquid
:3
The parabolic end-plate of the trough shown here is subjected to a fluid pressure that
varies linearly from 0 at its top to 100 lb/ft? at its bottom B, that is, p(y) = 100
-25y. Determine the magnitude of the resultant force on the end-plate.
2 ft
2 ft
y = x²
4 ft
B
O 501 Ib
O 271 Ib
O 314 Ib
O 427 Ib
O 623 Ib
The tank is filled with water. Suppose that h=4.0 m. Solve the problem using the integration method. Determine the resultant force acting on the trapezoidal plate C and determine the location of the center of pressure measured from the top of the tank.
Chapter 9 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
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