In a mixing tank operating at a very high Reynolds number 104, if the diameter of the im peller is doubled, keeping other conditions constant, the power required increases by a factor of:

Question

A soap bubble of radius \(r = 1\,\text{mm}\) is rising in a liquid of density \( \rho = 2000\,\text{kg/m}^3 \). At the instant the bubble is rising upward with constant velocity \(v = \tfrac{1}{2}\,\text{cm/s}\). Find the coefficient of viscosity \( (\eta) \).

Answer 1

In high Reynolds number mixing, power consumption is proportional to the impeller diameter raised to the fifth power:

\( P \propto D^5 \)

Therefore, doubling the impeller diameter results in a \( 2^5 = 32 \)-fold increase in power demand.

In a mixing tank operating at a very high Reynolds number 104, if the diameter of the im peller is doubled, keeping other conditions constant, the power required increases by a factor of:

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The Correct Option is D

Solution and Explanation

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