## Related questions with answers

Calculate the force $P$ necessary to hold the $\textrm{4-m}$ wide gate in the position shown in Fig. if: (a) $H=6 \mathrm{~m}$ (b) $H=8 \mathrm{~m}$ (c) $H=10 \mathrm{~m}$

Solution

VerifiedWe are asked to determine the required magnitude of the force $P$ to hold the gate in the given position.

First, we are going to formulate the equations for force $F$ and its location using the following equations.

$\begin{aligned} &F=\gamma\cdot\overline{h}\cdot A\hspace{4.4cm}\tag{1} \end{aligned}$

$\begin{aligned} &y_P=\overline{y}+\dfrac{\overline{I}}{A\cdot\overline{y}}\hspace{4.3cm}\tag{2} \end{aligned}$

where:

$\begin{aligned} F&=\text{force exerted by water}\\ \gamma&=\text{specific weight of water}\\ \overline{h}&=\text{vertical height from the centroid}\\ &\phantom{=}\text{of the gate to the water surface}\\ A&=\text{area of the figure}\\ y_P&=\text{distance from the center of pressure}\\ &\phantom{=}\text{on the gate to the water surface}\\ \overline{y}&=\text{distance from the centroid to the}\\ &\phantom{=}\text{water surface}\\ \overline{I}&=\text{second moment of area of the gate} \end{aligned}$

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