Total Hydrostatic Force on
Surfaces
Total Hydrostatic Force/Total Pressure
Total Hydrostatic Force/Total Pressure is defined as the force exerted
by a static fluid on a surface either plane or curved when the fluid comes
in contact with the surfaces. This force always acts normal to the surface.
Center of Pressure is defined as the point of application of the total
hydrostatic force on the surface.
There are four cases of submerged surfaces on which the total hydrostatic
force and center of pressure is to be determined. The submerged surfaces
maybe:
1. Horizontal plane surface
2. Vertical plane surface
3. Inclined plane surface
4. Curved surface
Horizontal Plane Surface
Vertical Plane Surface
FOR VERTICAL PLANE SUBMERGED UNDER A LIQUID SURFACE
Liquid Surface
Plane Surface
เดฅ= ๐
เดฅ
๐
๐๐
๐
๐
๐ญ
๐๐
๐
FOR INCLINED PLANE SUBMERGED UNDER A LIQUID SURFACE
Liquid Surface
เดฅ
๐
Plane Surface
Projection of Plane Surface
Curved surface
Curved surface
Sample Problems
Problem 1:
A vertical plane 10 m high and 3 m wide is submerged in a liquid having a specific gravity of 0.95. The top edge of
the plane is at the liquid surface. Determine the hydrostatics force F acting on one side of the plane and its
location from the liquid surface.
เดฅ
๐ญ = ๐ธ๐๐จ
Liquid Surface
Plane Surface
เดฅ= ๐
เดฅ
๐
เดฅ+๐
๐๐๐๐๐๐๐๐ ๐๐ ๐๐ = ๐
๐๐
๐๐
๐
๐๐
)(5๐)(10๐๐ฅ3๐)
๐3
๐ญ = ๐๐๐๐. ๐๐๐ ๐๐ต −− −๐๐๐๐๐๐
๐น = (0.95)(9.81
๐๐๐
๐. ๐๐๐๐๐ ๐
๐๐
๐๐
๐ญ
๐๐๐๐. ๐๐๐ ๐๐ต
๐ฐ๐
๐=
๐จเดฅ
๐
๐๐๐
๐ = ๐๐
๐๐เดฅ
๐
(๐)(๐๐๐ )
๐๐
๐=
(๐)(๐๐)(๐)
๐ = ๐. ๐๐๐๐๐ ๐
๐๐๐๐๐๐๐๐ ๐๐ ๐๐ = ๐๐ + ๐. ๐๐๐๐๐๐
= ๐. ๐๐๐๐๐๐ ๐๐๐๐ ๐๐๐๐๐๐
๐๐๐๐๐๐๐
Problem 2
In the figure shown, stop B will break if the force on it reaches 40 kN. Find the critical water depth. The length
of the gate perpendicular to the sketch is 1.5m.
L = 1.5 m
hinge
โเดค
h
0.5 m
F
e
cg
1m
cp
B
40 kN
าง
๐
= ๐๐กA
kN เดค
F = (9.81 3 )h(1m)(1.5m)
m
F = 14.715hเดค
๐๐
๐=
๐เดค
๐ฒ
๐คโ๐๐๐ ๐ฆเดค = โเดค
bh3
e = 12
bhเดคy
(1.5)(13 )
12
e=
(1.5)(1)hเดค
เท Moment at hinge = 0
F 0.5 + e = 40(1)
14.715hเดค 0.5 +
1
= 40(1)
เดค
12h
1
e=
12hเดค
hเดค = 5.27m
critical water depth
= 5.27m + 0.5m
= ๐. ๐๐๐ฆ
Problem 3:
A 30m long dam retains 9m of water as shown. Find the total hydrostatic force acting on the dam and the location
of the center of pressure from the bottom.
เดฅ=
๐
๐๐.๐๐๐
= 5.196m
๐
เดฅ = ๐. ๐๐
๐
๐๐๐๐๐๐
๐๐๐๐๐๐๐๐ ๐๐ ๐๐ = ๐ฟ = ๐. ๐๐๐ − ๐
๐=
๐ฐ๐
๐จเดฅ
๐
๐๐๐ ๐๐. ๐๐๐๐ ๐
๐๐
๐=
(๐๐๐)(๐๐. ๐๐๐๐)(๐. ๐๐๐๐)
๐ = ๐. ๐๐๐ ๐
เดฅ
๐ญ = ๐ธ๐๐จ
๐๐
๐น = (9.81 3 )(4.5๐)(10.392๐๐ฅ30๐)
๐
๐ญ = ๐๐๐๐๐. ๐๐๐๐ ๐๐ต −− −๐๐๐๐๐๐
๐๐๐๐๐๐๐๐ ๐๐ ๐๐ = ๐ฟ = ๐. ๐๐๐๐ − ๐. ๐๐๐๐
๐๐๐๐๐๐๐๐ ๐๐ ๐๐ = ๐ฟ = ๐. ๐๐๐๐ −−− −๐๐๐๐๐๐
Problem 4: Surface AB is a circular arc with a radius of 2 m and a width of 1
m into the paper. The distance EB is 4 m. The fluid above surface AB is water,
and atmospheric pressure prevails on the free surface of the water and on
the bottom side of surface AB. Find the magnitude and line of action of the
horizontal and vertical components of the total hydrostatic force acting on
surface AB.
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