Engineering Mechanics l
TEGT 3592
Forces in submerged surfaces
Lecturer
Dr. M. F. ERINOSHO
(Department of Mechanical and Industrial Engineering,
University of Namibia)
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Course Outlines
 Hydrostatic force
 Forces in submerged surfaces
 Water pressure acting on a bank or a sluice gate
 Surface Area, Centroid, and Moment of Inertia
of Certain Simple Geometrical Plates
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Hydrostatic forces on plane surface
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Forces in submerged surfaces
How large is the force acting on the whole face of a solid
wall subject to water pressure?
Basic conditions for a Plane surface submerged in a
fluid:
• Force on the surface is Perpendicular.
• Pressure is linearly dependent only on the vertical
depth.
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(1) On a Horizontal surface (e.g. the bottom of a tank)
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2. On an Inclined surface
Water pressure acting on a bank or a sluice gate
How large is the total force due to the water pressure
acting on a bank built at an angle (θ) to the water surface
of a dam?.
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Disregarding the atmospheric pressure, the pressure
acting on the surface is zero.
The total force dF acting on a small area dA is
dF = ρghdA = ρgysinθdA
Where h = ysinθ.
Integrating the resultant force, we obtain
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When the centroid of A is G, its y coordinate is yG and the
depth to G is hG,
The equation becomes
FR
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Let us consider a rectangular channel gate as shown below.
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The force F acting on the whole plane of the gate is
F = ρghGA
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The force F acting on a small area dA (i.e a horizontal strip
of the gate face) is
dF = ρgydA……..(1)
Then the moment of this force around the x axis is
= ρgydA x y…….(2)
The total moment on the gate is
……..(3)
is called the geometrical moment of inertia Ix,
for the x axis.
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The total moment on the gate is now
= ρgIx
The action point of F is now located at the centre of
pressure, (C) at which a single force F produces a moment
equal to the total sum of the moments around the turning
axis (x axis) of the gate produced by the total water
pressure.
When the location of C is yc,
Fyc = ρgIx …………(4)
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…………….(5)
When IG, is the geometrical moment of inertia of area for
the axis which is parallel to the x-axis and passes through
the centroid G, the following relation exist.
Substitute eqn (5) into (4) to calculate yc,
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Surface Area, Centroid, and Moment of Inertia of
Certain Simple Geometrical Plates
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EXAMPLE
A vertical trapezoidal gate with its upper edge located 5
m below the free surface of water is shown in Figure
2.10. Determine the total pressure force and the center
of pressure on the gate.
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The total pressure force is determined
The location of the center of pressure is
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EXAMPLE
An inverted semicircular gate is installed at 45o with respect
to the free water surface. The top of the gate is 5 ft below
the water surface in the vertical direction. Determine the
hydrostatic force and the center of pressure on the gate.
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The total pressure force is
Where
and
4x4
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Therefore
This is the total hydrostatic force acting on the gate. The
location of the center of pressure is
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Thank you
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