Gupta and Gupta $2\mathrm{.}6$

Example $2\mathrm{.}6.$ The automatic gate ABC shown in Fig. $2\mathrm{.}12($a$)$ is pivoted at

$B$ and opens by itself when the level $H$ exceeds $2m.$ What is the length

$BC?$

$\{$o$\}$

iv J

Fig. $2\mathrm{.}12($a$)$ Automatic gate for Example $2\mathrm{.}6,$ and $($b$)$ pressure distribution on it$.$

Find the pressure on $BC$

Find the resultant force $F_{R,BC}$

Find y$\text{'}$ using $y^{\text{'}}{F}_R={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$ypdA

Find the pressure at any point $($Use the coordinate system given in the book$)$

Find the resultant force $F_{R,AB}$

Use the moment balance $x^{\text{'}}{F}_{R,AB}=y^{\text{'}}{F}_{R,BC}$ to find $d.$