(Solved): Relation between downcomer area and weir length. Question A sieve-tray tower has an ID of 1.5m ...

Relation between downcomer area and weir length. Question A sieve-tray tower has an ID of $1.5\mathrm{m}\left(D_c\right)$, and the combined cross-sectional area of the holes of one tray $\left(A_h\right)$ is 10 per cent of the total cross-sectional area $\left(A_c\right)$ of the tower. The height of the weir $\left(h_w\right)$ is $50\mathrm{mm}$. The head of liquid over the top of the weir $(h_{\text{ow }}$ ) is $12\mathrm{mm}$. Liquid gradient on the tray is negligible. The diameter of the perforation $\left(d_h\right)$ is $5\mathrm{mm}$, and the superficial vapour velocity $\left(u_c\right)$ (based on the crosssectional area of the empty tower $\left(A_c\right)$ is $1.04\mathrm{m}/\mathrm{s}$. Take tray thickness $=$ hole diameter, and net area $\left(A_n\right)=92.5$ per cent of total area. Tray spacing $\left(I_t\right)$ is $0.5\mathrm{m}$. If the liquid density $\left({?}_I\right)$ is $810\mathrm{kg}/{\mathrm{m}}^3$ and the vapour density $\left({?}_{\mathrm{v}}\right)$ is $1.62\mathrm{kg}/{\mathrm{m}}^3$, 1) Estimate the pressure drop per tray $\left(h_t\right)$. 2) Estimate the downcomer backup ( ${\mathrm{h}}_{\mathrm{b}})$ and use it check whether the tray spacing is satisfactory or not. (Answer: $h_{\mathrm{t}}=92.3\mathrm{mm}$ liquid, ${\mathrm{h}}_{\mathrm{b}}=154.8\mathrm{mm}$ liquid)