Force on Plane Surfaces

Force on Plane Surfaces
The force on a plane surface submerged on a static fluid is the
hydrostatic force applied by the fluid on the surface.
If there is a plane surface of arbitrary shape submerged in a liquid, as
shown in the figure.?= angle of the plane surface inclination with the horizontal free surface.
h= the depth of any element area dA.
Pa= atmospheric pressure on the liquid surface.
The pressure on this area is:
P= Pa + ? h.
The hydrostatic force on one side of this area is :
F = Ptotal. A (1)
Ptotal= Pa + ? hCG (2)
Then the total hydrostatic force on one side of the plate is:
(4)
(5)
(6)
(7)
Pa is neglected because it acts on both sides of the plate.
So : PCG= ?hCG ;
And the force with center of pressure become
Example 1:
The resultant pressure force on a curved surface is computed by
separating it into horizontal and vertical components, as shown in the
Figure a.
Fig. b shows a free-body diagram of the column of fluid contained in the
vertical projection above the curved surface.
Forces on the vertical projection above the curved surface are:
1- FH & FV= pressure force components on the curved portion.
2- F1= pressure force on the vertical surface.
3- W1 & W2 = fluid weight over the curved surface
On the upper part bcde, the force (F1) is balanced by (F1) on the opposite
side.
On the lower part, the horizontal force is computed by:
FHPressure= horizontal component of (PCGA)
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