A water spray gun is attached to a hose of cross sectional area 30 cm². The gun comprises of 10 perforations each of cross sectional area of 15 mm². 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) (a) 100 m/s (b) 10 m/s (c) 1000 m/s (d) 15 × 10² m/s

Answer: (b). Continuity: A₁ v₁ = n a v (all perforations together). A₁ v₁ = 30 cm² × 50 cm/s = 1500 cm³/s = 1.5×10⁻³ m³/s na = 10 × 15 mm² = 150 mm² = 1.5×10⁻⁴ m² v = 1.5×10⁻³1.5×10⁻⁴ = 10 m/s So the answer is (b) 10 m/s.

A water spray gun is attached to a hose of cross sectional area 30… | JEE Main 2026 (4 Apr, Shift 2)

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Types of Flow, Reynolds Number & Continuity

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

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Answer: (b)

Continuity: $A_1 v_1 = n a v$ (all perforations together).
$A_1 v_1 = 30\text{ cm}^2 \times 50\text{ cm/s} = 1500\text{ cm}^3/\text{s} = 1.5\times10^{-3}\text{ m}^3/\text{s}$
$na = 10 \times 15\text{ mm}^2 = 150\text{ mm}^2 = 1.5\times10^{-4}\text{ m}^2$
$v = \dfrac{1.5\times10^{-3}}{1.5\times10^{-4}} = 10\text{ m/s}$
So the answer is (b) $10\text{ m/s}$ .

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