## Related questions with answers

Question

A force $P=300 ~\mathrm{kN}$ is needed to just open the gate of Fig. with $R=1.2 \mathrm{~m}$ and $H=4 \mathrm{~m}$. How wide is the gate? (A) $2.98 \mathrm{~m}$ (B) $3.67 \mathrm{~m}$ (C) $4.32 \mathrm{~m}$ (D) $5.16 \mathrm{~m}$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 4We are asked to determine the width *w* of the gate.

We will determine the width of the gate by getting the weight of the water that contributes to the hydrostatic force acting on the gate. The following equation will be used:

$\begin{aligned} &W=\rho\cdot V\hspace{2.8cm}\tag{1} \end{aligned}$

where:

$\begin{aligned} W&=\text{weight of the water}\\ \rho&=\text{specific weight of water}\\ V&=\text{volume of water} \end{aligned}$

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