Viscosity

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Question

The maximum speed of flow of water through a long cylindrical pipe of diameter 2cms so that the flow remains laminar is [ given that coefficient of viscosity of water $η = 10^{- 3} pa - s$ ]

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Solution

Flow remains laminar if $R_{e} < 2000$
$\begin{array}{l} i . e . \frac{ρ vd}{η} < 2000 \\ i . e \frac{10^{3} \times v \times 2 \times 10^{- 2}}{10^{- 3}} < 2000 \\ i . e v < 10^{- 1} m / s \\ \Rightarrow V_{\max} = 10 cm / s = 0 .1 m / s \end{array}$

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