Ncert Exercises & Solutions

10.16 The cylindrical tube of a spray pump has a cross-section of 8.0 cm² 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?

Given,

Area of cross-section of the pump, A₁ = 8 cm² = 8 × 10^–4 m²

Number of holes, n = 40

Radius of each hole, r = d/2 = 0.5 × 10^–3 m

Area of cross-section of each hole, a = ${πr}^{2}$ = $π$ (0.5 × 10^–3)² m²

Total area of 40 holes, A₂ = n × a = 40 × $π$ (0.5 × 10^–3)² m² = 31.41 × 10^–6 m²

Speed of flow of liquid inside the tube, v₁ = 1.5 m/min = 0.025 m/s

Let the speed of ejection of liquid through the holes is v_2.

According to the equation of continuity,

$A_{1} v_{1} = A_{2} v_{2} v_{2} = \frac{A_{1} v_{1}}{A_{2}} = \frac{8 \times 10^{- 4} \times 0.025}{31.61 \times 10^{- 6}}$

= 0.633 m/s

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