Question

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?

Answer 1

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

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 = πr² = 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

Speed of ejection of liquid through the holes = V₂

According to the law of continuity, we have:

= 0.633 m/s

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