First slide

Fluid dynamics

Question

A tank is filled up to a height 2H with a liquid and is placed on a platform of height H from the ground. The height x from the ground where a small hole is punched to get
the maximum range R is

Moderate

A

H
B

1.25 H
C

2H
D

1.5 H

Solution

$A s x = \frac{1}{2} g t^{2} \Rightarrow t = \sqrt{\frac{2 x}{g}}$
$V e l o c i t y o f e f f l u x v = \sqrt{2 g (3 H - x)}$
$Hence R = v t = 2 \sqrt{x (3 H - x)}$
$For range to be maximum \frac{d R}{d x} = 0$
$which gives x = \frac{3}{2} H = 1.5 H$

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