Propane gas is sent to an isothermal compressor at $1$atm absolute pressure and $50C$ and, after being compressed, is fed into a packed bed filled with $2\mathrm{.}5cm$ equivalent diameter Raschig rings as shown in Figure $2.$ Superficial velocity is given as $2\frac{m}{s}.$ The void fraction of the bed is $0\mathrm{.}65,$ the diameter of the bed is $0\mathrm{.}5m,$ and the bed height is $20m.$ If the outlet pressure of the gas from the bed is $1$atm, what should the pressure of the gas at the inlet of the bed be$?$ Also find the compressor work as kW$.$ The temperature and density of propane measured at $1$atm absolute pressure and $50C$ can also be considered constant throughout the bed. $M_{\text{p}\text{r}\text{o}\text{p}\text{a}\text{n}\text{e}}=44$

Figure $2$