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The speed of water is 2m/s through a pipe of internal diameter 10 cm. What should be the internal diameter of nozzle of the pipe if the speed of water at nozzle is 4 m/s2

in Chapter2:Mechanical Properties of Fluids by Expert (11.6k points) | 59 views

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Correct answer =7.07 x 10-2 m

Explaination::

Given : d1=10cm =0.1 m , v1=2m/s, v2=4m/s

Solution:

by the equation of continuity , the ratio of the speed is 

\(\frac{v1}{v2}=\frac{A2}{A1}=(\frac{d2}{d1})^2\) 

\(\therefore \frac{d2}{d1}=\sqrt{\frac{v1}{v2}} =\sqrt{\frac{2}{4}}\) \(=\frac{1}{\sqrt2}=0.707\) 

\(\therefore d2=0.707 d1\) \(=0.707(0.1m)=0.0707 m\) 

=7.07 x 10-2 m

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