Question

Consider a tray-column of diameter \( 120 \, \text{cm} \). Each downcomer has a cross-sectional area of \( 575 \, \text{cm}^2 \). For a tray, the percentage column cross-sectional area not available for vapour flow due to the downcomers, rounded off to 1 decimal place, is:

Hint:

For column design problems, calculate the total cross-sectional area and account for any obstructions like downcomers to estimate the effective area for vapour flow.

Answer 1

Step 1: Calculate the column cross-sectional area. The cross-sectional area of the column is: \[ A_\text{column} = \pi \left( \frac{D}{2} \right)^2, \] where \( D = 120 \, \text{cm} \) (column diameter). Substitute \( D = 120 \, \text{cm} \): \[ A_\text{column} = \pi \left( \frac{120}{2} \right)^2 = \pi (60)^2 = \pi \cdot 3600 \approx 11310 \, \text{cm}^2. \] Step 2: Total area occupied by downcomers. Assuming two downcomers, the total area occupied is: \[ A_\text{downcomers} = 2 \cdot 575 = 1150 \, \text{cm}^2. \] Step 3: Percentage area not available for vapour flow. The percentage area occupied by the downcomers is: \[ \%A_\text{not available} = \frac{A_\text{downcomers}}{A_\text{column}} \cdot 100. \] Substitute \( A_\text{downcomers} = 1150 \, \text{cm}^2 \) and \( A_\text{column} = 11310 \, \text{cm}^2 \): \[ \%A_\text{not available} = \frac{1150}{11310} \cdot 100 \approx 10.2\%. \] Step 4: Conclusion. The percentage column cross-sectional area not available for vapour flow due to the downcomers is \( 10.2\% \).