$7\mathrm{.}2.$ A catalyst tower $40$ ft high and $18$ ft in diameter is packed with $1-$in$.-$diameter spheres. Gas enters the top of the bed at a temperature of $450\backslash$deg F and leaves at the same temperature. The pressure at the bottom of the catalyst bed is $30$lb$,/$in$?$ abs$.$ The bed porosity is $0\mathrm{.}40.$ If the gas has average properties similar to propane and the time of contact $($based on flow in the void space$)$ between the gas and the catalyst is $8$ s$,$

what is the inlet pressure?