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TS EAMCET · Physics · Mechanical Properties of Fluids

What is the rate at which a trapped bubble of \(2 \mathrm{~mm}\) diameter rises slightly through a solution of density \(13.6 \times 10^3 \mathrm{~kg} / \mathrm{m}^3\) and coefficient of viscosity 1.5 centipoise? Assume, the density of air is negligible and \(g=10 \mathrm{~m} / \mathrm{s}^2\).

  1. A \(20 \mathrm{~m} / \mathrm{s}\)
  2. B \(2 \mathrm{~m} / \mathrm{s}\)
  3. C \(0.2 \mathrm{~m} / \mathrm{s}\)
  4. D \(0.02 \mathrm{~m} / \mathrm{s}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(20 \mathrm{~m} / \mathrm{s}\)

Step-by-step Solution

Detailed explanation

Emperical formula for velocity of small bubbles rising through a fluid is \[ v_{\text {terminal }}=1.15\left(\frac{g d\left(\rho_f-\rho_g\right)}{\eta_f}\right) \times 10^{-2} \] where, \(d=\) mean diameter, \(\rho_f=\) density of fluid, \(\rho_g=\) density of gas of bubble and…
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