Water is flowing continuously from a tap having an internal diameter 8 × 10⁻³ m. The water velocity as it leaves the tap is 0.4 ms⁻¹. The diameter of the water stream at a distance 2 × 10⁻¹ m below the tap is close to: (a) 7.5 × 10⁻³ m (b) 9.6 × 10⁻³ m (c) 3.6 × 10⁻³ m (d) 5.0 × 10⁻³ m

Answer: (c). Speed at h = 0.2 m below: v² = (0.4)² + 2×10×0.2 = 4.16 ⇒ v ≈ 2.04 m/s Continuity: d₁² v₁ = d₂² v₂ ⇒ d₂ = d₁√((v₁)/(v₂)) d₂ = 8×10⁻³√((0.4)/(2.04)) ≈ 8×10⁻³×0.44 ≈ 3.6×10⁻³ m So the answer is (c).

Water is flowing continuously from a tap having an internal diameter… | JEE Main 2011 (AIEEE)

Q22JEE Main 2011 · AIEEEMedium

Types of Flow, Reynolds Number & Continuity

Water is flowing continuously from a tap having an internal diameter $8 \times 10^{-3}\text{ m.}$ The water velocity as it leaves the tap is $0.4\text{ ms}^{-1}$ . The diameter of the water stream at a distance $2 \times 10^{-1}\text{ m}$ below the tap is close to:

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Answer: (c)

Speed at $h = 0.2\text{ m}$ below: $v^2 = (0.4)^2 + 2\times10\times0.2 = 4.16 \Rightarrow v \approx 2.04\text{ m/s}$
Continuity: $d_1^2 v_1 = d_2^2 v_2 \Rightarrow d_2 = d_1\sqrt{\dfrac{v_1}{v_2}}$
$d_2 = 8\times10^{-3}\sqrt{\dfrac{0.4}{2.04}} \approx 8\times10^{-3}\times0.44 \approx 3.6\times10^{-3}\text{ m}$
So the answer is (c).

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