Fluid Mechanics Problems 2
Consider a gate
CD
, which is shown below and can be (a) rectangular, (b) circular, and (c) triangular
in shape. The gate is only hinged at the top, and has no support elsewhere. Find the moment to be
applied at the hinge in each case to keep the gate in equilibrium. Density of water = 1,000 kg/m
3
.
D
C
air
hinge
water
5 m
6 m
2 m
6 m
sectional view
front view
Rectangluar gate
Circular gate
Triangular gate
Area of the gate (
A
)
Depth of the center of
area (
h
c
)
Magnitude of the
resultant force due to
hydrostatic pressure on
the gate
F
R
=
Second moment of area
about the horizontal
axis through the center
of area (
I
c
)
Depth of the center of
pressure
h
R
=
Applied moment about
the hinge to keep the
gate in equilibrium
M
=
For each part, write down the formula (or give the right-hand side of the equation) before plugging in.
State clearly the units and the direction of the moment.

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