A water spray gun is attached to a hose of cross sectional area 30 cm ^2 . The gun comprises of 10 perforations each of cross sectional area 15 mm ^2 . If the water flows in the hose with the speed of 50 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

Step-by-step solution

From the equation of continuity: A₁ v₁ = n A₂ v₂ Here, A₁ = 30 cm ^2 = 30 10⁻⁴ m ^2 v₁ = 50 cm/s = 0.5 m/s n = 10 A₂ = 15 mm ^2 = 15 10⁻⁶ m ^2 Substituting the given values: (30 10⁻⁴) 0.5 = 10 (15 10⁻⁶) v₂ 15 10⁻⁴ = 150 10⁻⁶ v₂ 15 10⁻⁴ = 1.5 10⁻⁴ v₂ v₂ = 15 10⁻⁴ 1.5 10⁻⁴ = 10 m/s Answer: 10 m/s