Water is flowing continuously from a tap having internal diameter 8 × 10^-3m. The water velocity as it leaves the tap is 0.4 ms^-1. The diameter of the water stream at a distance 2 × 10^-1m below the tap is close to

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7.5 × 10^-3m

9.6 × 10^-3m

3.6 × 10^-3m

5.0 × 10^-3m

answer is C.

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Detailed Solution

From Bernoulli’s theorem, $ρgh = \frac{1}{2} ρ (v_{2}^{2} - v_{1}^{2})$
$\begin{array}{l} A_{1} v_{1} = A_{2} v_{2}; D_{1}^{2} v_{1} = D_{2}^{2} v_{2} (D = pipe diameter) \\ V_{2} = \sqrt{V_{1}^{2} + 2 gh} \end{array}$

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