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The face of a dam is vertical to a depth of 17m below the water surface from slopes at $60^{\large\circ}$ to the vertical.If the depth of water is 7.5m.What is the $F_{resultant}$ on the whole face?

$\begin{array}{1 1}(A)\;1561KN\\(B)\;1563.29KN\\(C)\;1326.3KN\\(D)\;1389KN\end{array} $

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$h_2=17m$,so $h_1=17-7.5=9.5m$
$x=\large\frac{9.5}{\tan 60^{\\large\circ}}=$$5.485$
Vertical force =Wt.of water above the surface
$F_V=\rho g(h-2\times x+0.5 h_1 x)$
$\Rightarrow 9810\times (7.5\times 5.485+0.5\times 9.5\times 5.485)$
$\Rightarrow 659.123KN/m$
$F_H=$Force on the projection of the surface on to a vertical plane
$\;\;\;\;\;\;=\large\frac{1}{2}$$\rho g h^2$
$\;\;\;\;\;\;=1417.545KN/m$
$F_R=1563.29KN/m$
Hence (B) is the correct answer.
answered May 9, 2014 by sreemathi.v
 

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