First slide

Viscosity

Question

A liquid having viscosity $η$ and density $ρ$ is flowing through a pipe of diameter d and its critical velocity is found to be 0.8 m/s. Then critical velocity of another liquid having coefficient of viscosity $η / 2$ , density $ρ / 2$ flowing through a pipe of diameter d/2 will be

Moderate

A

1.6 m/s
B

2.2 m/s
C

0.4 m/s
D

1.2 m/s

Solution

$\begin{array}{l} \frac{{ρV}_{cr} . d}{η} = R_{e} \Rightarrow V_{cr} = \frac{{ηR}_{e}}{ρd} \\ ∴ \frac{V_{cr}^{1}}{V} = (\frac{η^{1}}{η}) (\frac{ρ}{ρ^{1}}) (\frac{d}{d^{1}}) \\ \Rightarrow \frac{V_{cr}^{1}}{0 .8} = (\frac{1}{2}) (2) (2) \Rightarrow V_{cr}^{1} = 1 .6 m / s \end{array}$

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