If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter $\frac{2}{\sqrt{π}}$ cm then the Reynolds number for the flow is (density of water= $10^{3} K g / m^{3}$ ) and viscosity of water= $10^{- 3} p a . s$ )close to:

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5500

11000

1100

550

answer is D.

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Detailed Solution

$\begin{array}{l} R = \frac{ρVD}{η} r = \frac{D}{2} = \frac{1}{\sqrt{π}} = R = \frac{2}{\sqrt{π}} \\ 15 \times 10^{- 3} m^{3} \to 5 \min = 5 \times 60 \sec \\ Rate of flow = \frac{15 \times 10^{- 3}}{5 \times 60} = A \times V \\ \frac{1}{20} \times 10^{- 3} = π \times \frac{1}{π} \times 10^{- 4} v \end{array}$

$\begin{array}{l} V = 0.5 \\ R = \frac{10^{3} \times 0.5 \times \frac{2}{\sqrt{π}} \times 10^{- 2}}{10^{- 3}} \\ = 0.55 \times 10^{4} \\ = 5500 \end{array}$