Question

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 the flooding velocity (\(u_{0,F}\)). The ratio of the allowable mass velocity of the vapor in packing P to that in packing Q is ______ (rounded off to one decimal place).

Hint:

The 0.6 factor, gas density and the density-difference term all cancel in the ratio; you only need the chart's Y-value ratio for packing P versus packing Q at the computed flow parameter.

Answer 1

Correct Answer: 1.5

Step 1: Identify the flooding correlation.
For the generalized flooding correlation used with structured packings, the chart plots a capacity parameter on the y-axis against a flow parameter on the x-axis:
\[ Y = u_{0,F}\sqrt{\frac{\rho_y}{\rho_x-\rho_y}}, \qquad X = \frac{G_x}{G_y}\sqrt{\frac{\rho_y}{\rho_x}} \]
where \(u_{0,F}\) is the superficial gas (vapor) velocity at flooding, \(G_x\) and \(G_y\) are the liquid and gas mass velocities, and \(\rho_x\), \(\rho_y\) are the liquid and gas densities.

Step 2: Calculate the flow parameter X.
Given \(G_x/G_y = 1.27\), \(\rho_y = 1.2\ kg\ m^{-3}\), \(\rho_x = 1200\ kg\ m^{-3}\):
\[ X = 1.27\sqrt{\frac{1.2}{1200}} = 1.27\sqrt{0.001} = 1.27 \times 0.0316 = 0.0402 \]

Step 3: Read the capacity parameter for each packing at X = 0.0402.
From the flooding chart, moving vertically up from X = 0.0402 on the log-log plot to the two curves:
Packing P (upper curve): \(Y_P \approx 0.116\)
Packing Q (lower curve): \(Y_Q \approx 0.077\)

Step 4: Since the density terms, the 60% factor, and gas density are identical for both packings, they cancel in the ratio:
\[ \frac{G_{y,allow,P}}{G_{y,allow,Q}} = \frac{Y_P}{Y_Q} = \frac{0.116}{0.077} \approx 1.5 \]

\[ \boxed{\frac{G_{y,allow,P}}{G_{y,allow,Q}} \approx 1.5} \]