## Related questions with answers

At what height $H$ will the rigid gate, hinged at a central point as shown in Fig., open if $h$ is: (a) $0.6 \mathrm{~m}$ ? (b) $0.8 \mathrm{~m}$ ? (c) $1.0 \mathrm{~m} ?$

Solution

VerifiedWe are asked to determine the height $H$ required to open the gate.

We will analyze the figure given to point where the force $F$ exerted by water should be located that will cause the gate to start opening. We will then use the following equation to determine the height $H$ required:

$\begin{aligned} &y_P=\overline{y}+\dfrac{\overline{I}}{A\cdot\overline{y}}\hspace{4.3cm}\tag{1} \end{aligned}$

where:

$\begin{aligned} y_P&=\text{distance from the center of pressure}\\ &\phantom{=}\text{on the gate to the water surface}\\ \overline{y}&=\text{distance from the centroid to the}\\ &\phantom{=}\text{water surface}\\ \overline{I}&=\text{second moment of area of the gate}\\ A&=\text{area of the figure}\hspace{3.2cm} \end{aligned}$

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