Question 2.22: A sloping plane with a width of 1 ft and a length of 3ft is ...

A sloping plane with a width of 1 ft and a length of 3ft is submerged in a gas tank and subjected to a gas pressure of 8 psi, as illustrated in Figure EP 2.22. (a) Determine the magnitude of the resultant hydrostatic force acting on the sloping plane. (b) Determine the location of the resultant hydrostatic force acting on the sloping plane.

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(a) The magnitude of the hydrostatic resultant force acting on the sloping plane is determined by applying Equation 2.111 F=pA as follows:

W:=1ft                     L:=3ft                     A:=w.L = 3ft^{2}
P_{g} :=8 \frac{lb}{in^{2} } \frac{(12in)^{2} }{(1in)^{2}} =1.152 \times 10^{3} \frac{Ib}{ft^{2} }                                 F:=P_{g}.A=3.456 \times 10^{3} lb

(b) The location of the resultant hydrostatic force acting on the sloping plane is located at the center of area of the sloping rectangular plane and is computed as follows:

y_{ca} :=\frac{L}{2} =1.5 ft                         y_{F}:=y_{ca}=1.5ft

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