Question

The cylindrical tube of a spray pump has a cross-section of 8.0 cm², one end of which has 40 line holes each of diameter 1.0 mm. If the liquid flows inside the tube is 1.5 m min^-1. What is the speed of ejection of the liquid through the holes?

Answer 1

Here area of cylindrical tube

a₁ = 8.0 cm² = 8 x 10³ m²

Velocity of flow, v₁ = 1.5 m min^-1

= 1.5/60 ms^-1 = 2.5 x 10^-2 ms^-1

Area of each hole = πD²/4 = {3.14 x (1 x 10^-3)²}/{4} = 7.85 x 10^-7 m²

Total area of all the 40 holes is,

a₂ = 40 x 7.85 x 10^-7 m² = 3.14 x 10^-5 m²

If v₂ is the velocity of ejection of liquid, then from the continuity equation,

a₁v₁ = a₂v₂

⇒ v₂ = {a₁v₂}/{a₂} = {8 x 10^-4 x 2.5 x 10^-2}/{3.14 x 10^-5}

= 0.637 ms^-1 = 0.64 ms^-1