First slide

Fluid dynamics

Question

Water is flowing continuously from a tap having an internal diameter 8 × 10^–3 m.The water velocity as it leaves the tap is 0.4 ms^–1. The diameter of the water stream at a distance 2 × 10^–1m below the tap is close to :

Moderate

A

7.5 x 10^-3 m
B

9.6 x 10^-3 m
C

3.6 x 10^-3 m
D

5.0 x 10^-3 m

Solution

$\large d_1=8\times10^{-3}m;\;r_1=4\times10^{-3}\;m$
$\large V_1=0.4m/s;\;h=2\times10^{-1}m;\;A_1V_1=A_2V_2$
$\large r_1^2V_1=r_2^2V_2\;and\;V_2=\sqrt {V_1^2+2gh}$
$\large \therefore r_2^2 =r_1^2\frac {V_1}{\sqrt {V_1^2+2gh}}=\frac {(4\times10^{-3})^2\times 0.4}{\sqrt {0.16+2\times9.8\times 2\times 10^{-1}}}$
$\large =3.6\times 10^{-3}\;m$

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