Class 12 Maharashtra State Board

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/s?

The given data that can be listed from the question is,

$https://latex.codecogs.com/svg.image? \mathrm{v_{1}= 2m/s}$

$https://latex.codecogs.com/svg.image? \mathrm{d_{1}= 10cm= 0.1m}$

$https://latex.codecogs.com/svg.image? \mathrm{v_{2}= 4m/s}$

To find, internal diameter

$https://latex.codecogs.com/svg.image? \mathrm{d_{2}= ?}$

Solution -

As per the equation of continuity we have

$https://latex.codecogs.com/svg.image? \mathrm{A_{1}v_{1} = A_{2}v_{2}}$

$https://latex.codecogs.com/svg.image? \mathrm{\frac{v_{1}}{v_{2}} = \frac{A_{2}}{A_{1}}}$

$https://latex.codecogs.com/svg.image? \mathrm{\frac{v_{1}}{v_{2}} = (\frac{d_{2}}{d_{1}})^{2}}$

$https://latex.codecogs.com/svg.image?\mathrm{\frac{d_{2}}{d_{1}} = \sqrt{\frac{v_{1}}{v_{2}}}$

$https://latex.codecogs.com/svg.image?\mathrm{\frac{d_{2}}{d_{1}} = \sqrt{\frac{2}{4}}}= 0.707$

$https://latex.codecogs.com/svg.image?\mathrm{d_{2}= 0.707 d _{1}}= 0.707 \mathrm{x 0.1} = 0.0707 m$

the internal diameter is 0.0707m