The cylindrical tube of a spray pump has a cross-section of 6 ${\mathrm{cm}}^2$ one of which has 50 holes each of diameter I mm. If the liquid flow inside the tube is 1.2 m per minute, then the speed of ejection of the liquid through the holes is

Here, area of cross section of tube

${\mathrm{a}}_1 = 6 {\mathrm{cm}}^2 = 6 \times {10}^{-4} {\mathrm{m}}^2$

Number of holes = 50

Diameter of each hole, D = 1 mm = ${10}^{-3}$m

Radius of hole, r = $\frac{\mathrm{D}}{2} = \frac{1}{2}\times {10}^{-3} = 5 \times {10}^{-4} \mathrm{m}$

Area of cross-section of each hole

  = ${\mathrm{\pi r}}^2 = \mathrm{\pi }{(5\times {10}^{-4})}^2 {\mathrm{m}}^2$

Total area of cross-section of 50 holes,

$a_2 = 50 \times \mathrm{\pi }{(5\times {10}^{-4})}^2 {\mathrm{m}}^2$

Speed of liquid inside the tube,

${\mathrm{v}}_1= 1.2 \mathrm{m} {\min }^{-1}$

 $= \frac{1.2}{60}{\mathrm{ms}}^{-1} = 0.02 {\mathrm{ms}}^{-1}$

Let the velocity of ejection of the liquid through the hole ${\text{v}}_2$

As ${\mathrm{a}}_1{\mathrm{v}}_1 = {\mathrm{a}}_2{\mathrm{v}}_2$

or ${\mathrm{v}}_2 = \frac{{\mathrm{a}}_1{\mathrm{v}}_1}{{\mathrm{a}}_2} = \frac{6\times {10}^{-4}\times 0.02}{50\times \mathrm{\pi }{(5\times {10}^{-4})}^2} = 0.31 {\mathrm{ms}}^{-1}$