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

Number of holes = 40

Diameter of each hole, D = 10^-3m

Area of cross section of each hole

Total area of cross section of 40 holes,

a₂ = \(\frac {40 \times π \times10^{-6}}{4}\)

= π × 10^-5m²

speed of liquid inside the tube,

V₁ = 1.5 m/min = 1.5/60 m/s

Area of cross section of tube,

a₁ = 8.0cm² = 8 × 10^-4m²

If V₂ is the velocity of ejection of liquid through the holes then from equation of continuity,

a₁ v₁ = a₂ v₂

⇒ v₂  

⇒ v₂ = 0.637 m/s

∴ the speed of ejection is 0.637 m/s.