GATE 2026 CH – Question 61

Mass Transfer · Absorption · 2 marks · Numerical answer

The flooding velocity curves for two different structured packings are shown in the figure. The ratio of mass velocities of liquid ($G_x$) to that of the gas ($G_y$) is 1.27. The density of the liquid ($\rho_x$) is 1200 kg m$^{-3}$ and that of the gas ($\rho_y$) is 1.2 kg m$^{-3}$. For both the packings, the allowable superficial vapor velocity is 60% of flooding velocity ($u_{0,F}$). The ratio of allowable mass velocity of the vapor in packing P to that in packing Q is _____________ (rounded off to one decimal place).

a log-log plot of $u_{0,F}\sqrt{\rho_y/(\rho_x - \rho_y)}$ (from 0.02 to 0.2) against $\frac{G_x}{G_y}\sqrt{\rho_y/\rho_x}$ (from 0.01 to 1). Packing P is a falling curve starting at about 0.135 at 0.01 and reaching about 0.10 at 0.1. Packing Q is a lower falling curve starting at about 0.09 at 0.01 and reaching about 0.066 at 0.1.

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Correct answer: 1.49 to 1.51

Explanation

The abscissa is $\frac{G_x}{G_y}\sqrt{\frac{\rho_y}{\rho_x}} = 1.27\sqrt{\frac{1.2}{1200}} = 0.0402$. At this value the curve for packing P reads about 0.119 and the curve for packing Q reads about 0.081 on the vertical axis. The densities are the same, so the flooding velocity is proportional to the ordinate. The allowable vapour velocity is 60 % of flooding for both, and the mass velocity of the vapour is velocity times density, so the ratio of allowable mass velocities is the ratio of the ordinates: $\frac{0.119}{0.081} \approx 1.5$.