Fluid Mechanics

JEE Main level, single correct, medium

77 of 192

Question 77 of 192

Water is flowing continuously from a tap having an internal diameter 8×10−3 m8 \times 10^{-3} \mathrm{~m}. The water velocity as it leaves the tap is 0.4 ms−10.4 \mathrm{~ms}^{-1}. The diameter of the water stream at a distance 2×10−1 m2 \times 10^{-1} \mathrm{~m} below the lap is close to :

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Answer: (C) 3.6×10−3 m3.6 \times 10^{-3} \mathrm{~m}

Equation of continuity
⇒(a×v) top =(a×v) bottom vb2−(0.4)2=2×9.8×0.2[v2−u2=2gh is used ]vb=2 m/s (nearly) π[8×10−3]×0.4=πd2×4 d≈3.6×10−3 m\begin{aligned} & \Rightarrow(\mathrm{a} \times \mathrm{v}) \text { top }=(\mathrm{a} \times \mathrm{v}) \text { bottom } \\ & \mathrm{v}_{\mathrm{b}}^2-(0.4)^2=2 \times 9.8 \times 0.2\left[\mathrm{v}^2-\mathrm{u}^2=2 \mathrm{gh} \text { is used }\right] \\ & \mathrm{v}_{\mathrm{b}}=2 \mathrm{~m} / \mathrm{s} \text { (nearly) } \\ & \pi\left[8 \times 10^{-3}\right] \times 0.4=\pi \mathrm{d}^2 \times 4 \\ & \mathrm{~d} \approx 3.6 \times 10^{-3} \mathrm{~m} \end{aligned}

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