First slide

Fluid dynamics

Question

A water tank of height H, completely filled with water is placed on a level ground. It has two holes one at a depth h from top and the other at height h form its base. The water ejecting from both holes

Moderate

A

both the holes will fall at the same spot
B

upper hole will fall farther than that from the lower
hole
C

upper hole will fall closer then that from the lower hole
D

more information is required.

Solution

Velocity of water coming out from hole I
= $v_{1} = \sqrt{2 gh}$
Velocity of water coming out from hole B
= $v_{2} = \sqrt{2 g (H - h)}$
Time taken by water to reach the ground from hole I
= $t_{1} = \sqrt{\frac{2 (H - h)}{g}}$
Time taken by water to reach the ground from hole B
= $t_{2} = \sqrt{\frac{2 h}{g}}$
Obviously, range on the ground for both is the same
$∴$ R = $v_{1} t_{1} = v_{2} t_{2} = 2 g \sqrt{h (H - h)}$

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