Hydrostatic
Forces on Submerged Plates
The elemental pressure force dF acting on the
element of area dA
is dF = PdA. Now the pressure, P, varies linearly with depth,
x. So
P = γ x and the differential
pressure force is dF = =
γ x dA
. So integration gives the total
hydrostatic pressure force, F.
F
= ∫ γ x dA ˗ ˗ ˗ ˗ ˗ (1) Note from the principle of first moments A xcg
= ∫ x dA
so γA
xcg = γ ∫ x dA . Also γ xcg is the pressure at the centroid
of the area of the plate. So F
= (γ xcg
) A (total hydrostatic pressure force
equals pressure at the centroid of plate times
total area of the plate) Click here to determine the location of the total hydrostatic
pressure force acting on the plate. |
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