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GATE 2023 CH – Question 26

Mass Transfer · Distillation · 1 mark · Multiple choice

A packed distillation column, with vapor having an average molecular weight of 45 kg kmol$^{-1}$, density of 2 kg m$^{-3}$ and a molar flow rate of 0.1 kmol s$^{-1}$, has a flooding velocity of 0.15 m s$^{-1}$. The column is designed to operate at 60% of the flooding velocity. Which one of the following is the CORRECT value for the column diameter (in m)?

  1. $\frac{5}{\sqrt{\pi}}$
  2. $5\sqrt{\pi}$
  3. $\frac{4}{\pi}$
  4. $\frac{10}{\sqrt{\pi}}$

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Correct answer: (D) $\frac{10}{\sqrt{\pi}}$

Explanation

The design velocity is $0.6 \times 0.15 = 0.09$ m/s. The mass flow of the vapour is $0.1 \times 45 = 4.5$ kg/s, which is a volume flow of $\frac{4.5}{2} = 2.25$ m³/s. The area is $\frac{2.25}{0.09} = 25$ m², so $\frac{\pi}{4}D^2 = 25$ and $D = \sqrt{\frac{100}{\pi}} = \frac{10}{\sqrt{\pi}}$ m.