First slide

Fluid dynamics

Question

A long cylindrical tank of radius I m is being filled by a pipe of radius 2 cm. The incoming water has a velocity of l m/s. The tank has a hole of radius l cm at the bottom. What is the height of water in the tank in steady state?

Easy

A

0.4 m
B

0.6 m
C

0.8 m
D

the level will continue to increase

Solution

In steady state, $A_{1} v_{1} = A_{2} v_{2}$
$π \times 2^{2} \times 1 = π \times 1^{2} \times \sqrt{2 gh}$
$\Rightarrow h = \frac{16}{20} = 0.8 m$

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