Question 2.30: A horizontal circular plane with a diameter of 5 ft is subme...

(a) The magnitude of the hydrostatic resultant force acting on the horizontal plane is determined by applying Equation 2.180 F = F_{G} = \gamma HA= \gamma H (\frac{\pi D^{2} }{4} ) as follows:

D:= 5 ft                     A:= \frac{\pi .D^{2} }{4} = 19.365 ft^{2}                     H:=9 ft
\gamma :=62.417 \frac{Ib}{ft^{3} }                     F_{G} := \gamma HA= 1.103 \times 10^{4} Ib                     F:= F_{G} =1.103 \times 10^{4} Ib

Alternatively, the magnitude of the hydrostatic resultant force acting on the horizontal plane is determined by applying Equation 2.181 F= p_{ca} A = \gamma h_{ca}A = \gamma (H)(\frac{\pi D^{2} }{4} ) as follows:

h_{ca} := H = 9ft                    F:= \gamma h_{ca}A = 1.103 \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 circular plane and is computed as follows:

h_{F}: = h_{ca} = 9 ft                       \frac{D}{2} = 2.5 ft