Question 2.31: A horizontal triangular plane with a base of 6 ft and a heig...

(a) The magnitude of the hydrostatic resultant force acting on the horizontal plane is determined by applying Equation 2.182 F= F_{G} = \gamma HA= \gamma H (\frac{BL}{2} ) as follows:

B:= 6 ft                  L:= 8 ft                  A:= \frac{BL}{2} = 24 ft^{2}                  H:= 11 ft
\gamma := 62.417 \frac{Ib}{ft^{3} }                  F_{G} = \gamma HA= 1.648 \times 10^{4} Ib                  F:= F_{G} 1.648 \times 10^{4} Ib

Alternatively, the magnitude of the hydrostatic resultant force acting on the horizontal plane is determined by applying Equation 2.183 F = p_{ca} = \gamma h_{ca} A = \gamma (H)(\frac{BL}{2} ) as follows:

h_{ca} := H=11 ft                  F:= \gamma h_{ca}A= 1.648 \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 triangular plane and is computed as follows:

h_{F}:= h_{ca}=11 ft                          \frac{2L}{3} = 5.333 ft                        \frac{L}{3} = 2.667 ft