Question 2.26: A horizontal plane with a width of 2 ft and a length of 5 ft...

(a) The magnitude of the hydrostatic resultant force acting on the horizontal plane is determined by applying Equation 2.154 f=F_{G} +p_{g}A=\gamma HA+p_{g}A=\gamma HwL+p_{g}wL=(\gamma H+p_{g})(wL) as follows:

W:= 2ft               L:= 5ft               A:= w.L = 10 ft^{2}                H :=7ft               \gamma :=62.417 \frac{Ib}{ft^{3} }

F_{G}:=\gamma .H.A=4.369\times 10^{3} Ib             p_{g}:=10 \frac{Ib}{in^{2} }\frac{(12in)^{2} }{(1in)^{2}} =1.44\times 10^{3} \frac{Ib}{ft^{2} }
F:= F_{G}+p_{g}.A=1.877 \times 10^{4} Ib

Alternatively, the magnitude of the hydrostatic resultant force acting on the horizontal plane is determined by applying Equation 2.155 F=(p_{ca}+p_{g})A=(\gamma h_{ca}+p_{g})A=(\gamma H+p_{g})(wL) as follows:

h_{ca}:= H = 7ft           F:= (\gamma h_{ca}+p_{g}) A=1.877 \times 10^{4} Ib

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

h_{F}:=h_{ca}=7ft                       \frac{L}{2}=2.5 ft                       \frac{W}{2}=1 ft