__Question 10.16__:^{2}one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min

^{–1}, what is the speed of ejection of the liquid through the holes?

__Solution__:*A*

_{1}= 8 cm

^{2 }= 8 × 10

^{–4}m

^{2}

Number of holes,

*n*= 40

Diameter of each hole,

*d*= 1 mm = 1 × 10

^{–3}m

Radius of each hole,

*r*=

*d*/2 = 0.5 × 10

^{–3}m

Area of cross-section of each hole,

*a*= π

*r*

^{2 }= π (0.5 × 10

^{–3})

^{2}m

^{2}

Total area of 40 holes,

*A*

_{2 }=

*n*×

*a*

= 40 × π (0.5 × 10

^{–3})

^{2}m

^{2}

= 31.41 × 10

^{–6}m

^{2}

Speed of flow of liquid inside the tube,

*V*

_{1 }= 1.5 m/min = 0.025 m/s

Speed of ejection of liquid through the holes =

*V*

_{2}

According to the law of continuity, we have:

A

_{1}V

_{1}= A

_{2}V

_{2}

V

_{2}= A

_{1}V

_{1}/ A

_{2}

= 8 X 10

^{-4}X 0.025 / (31.61 X 10

^{-}

^{6})

= 0.633 m/s

Therefore, the speed of ejection of the liquid through the holes is 0.633 m/s.

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