a liquid is filled in a container as shown in figure, there is a circular area on the side wall at depth h/4. Radius of circular area is h/8, where h is height of container area. Find force applied by liquid on circular area.
(assume container is filled completely)
Answers
Answer:
Pressure is defined as the force per unit area:
P
=
F
A
.
If an object is immersed in a liquid at a depth
h
, the fluid pressure is given by the constant depth formula
P
=
ρ
g
h
,
where
ρ
is the fluid density and
g
is the acceleration due to gravity.
Fluid pressure is a scalar quantity. It has no direction, so a fluid exerts pressure equally in all directions. This statement is known as Pascal’s law discovered by the French scientist Blaise Pascal (
1623
−
1662
).
Consider the case when a vertical plate bounded by the lines
x
=
a
,
x
=
b
,
y
=
f
(
x
)
,
y
=
g
(
x
)
is immersed in a liquid.
Fluid force acting on a lamina immersed in a liquid.
Figure 1.
Since the different points of the lamina are at different depths, the total hydrostatic force
F
acting on the lamina is determined through integration:
F
=
ρ
g
b
∫
a
[
f
(
x
)
−
g
(
x
)
]
x
d
x
.
This formula is often referred as the variable depth formula for fluid force.
Explanation:
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