A tank of height 15m and cross-section area 10 m² is filled with water. There is a small hole of cross-section area a which is much smaller than the container, located at a height of 12m from the base of the container. How much force should be applied with a piston at the top level, so that the water coming out of the hole hits the ground at a distance of 16m? (Take, density of water $= 1000 {kg m}^{- 3}$ )

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233 kN

200 kN

320 kN

400 kN

answer is A.

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Detailed Solution

As, range of water jet = 16 m.
If velocity of efflux is v, then
$v \times \sqrt{\frac{2 H}{g}} = 16$ , where H = 12 m.
Question Image
Also, $v = \sqrt{2 g h + \frac{2 (p - p_{o})}{ρ}}, 1000 k g - m^{- 1}$
and $h = 3 m$
so combining these, we get
$(2 g h + \frac{2 (p - p_{a})}{ρ}) (\frac{2 H}{g}) = 256$
$\Rightarrow 2 \times 10 \times 3 + \frac{2 Δ p}{1000} = \frac{2560}{2 \times 12} \Rightarrow Δ p = 23.3 k \frac{N}{m^{2}}$
so, force applied = $Δ p \times A = 233 k N$