A sieve tray column with \(0.4572-\mathrm{m}\) tray spacing is designed to operate at \(p=4.0 \mathrm{~atm}\). The value of the flow parameter is \(\mathrm{F}_{1 \mathrm{v}}=0.71\), and the flooding velocity was calculated as \(\mathrm{u}_{\text {flood }}=1.29 \mathrm{~m} / \mathrm{s}\). Unfortunately, the latest lab results show that the reboiler temperature is too high, and unacceptable thermal degradation occurs. To reduce the operating temperature, you plan to reduce the column pressure to \(1.0 \mathrm{~atm}\).

a. Estimate the new flooding velocity.

b. If the old system required a 4.0 -ft diameter column, for the same feed rate and same fraction of flooding, what column diameter is required for the new system?

Assumptions: Ideal gas, and relative volatility \(\alpha, \sigma, \eta\), and \(ho_{\mathrm{L}}\) are unchanged, \(ho_{\mathrm{L}} \gg>ho_{\mathrm{V}}\) (thus, \(ho_{\mathrm{L}}-ho_{\mathrm{V}}=ho_{\mathrm{L}}\) ). To estimate the effect of pressure on temperature, assume that the compound is essentially pure in the reboiler and it has the same \(\mathrm{K}\) value as n-octane.