First slide

Fluid dynamics

Question

Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of flow of water in the pipe of 2 cm diameter is

Easy

A

4 times that in the other pipe
B

$\frac{1}{4}$ times that in the other pipe
C

2 times that in the other pipe
D

$\frac{1}{2}$ times that in the other pipe

Solution

$d_{A} = 2 cm$ and $d_{B} = 4 cm$
$∴ r_{A} = 1 cm$ and $r_{B} = 2 cm$
From equation of continuity, av = constant
$∴ \frac{v_{A}}{v_{B}} = \frac{a_{B}}{a_{A}} = \frac{π {(r_{B})}^{2}}{π {(r_{A})}^{2}} = {(\frac{2}{1})}^{2} \Rightarrow v_{A} = 4 v_{B}$

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