PROBLEM $5(20\%)$

A wet sludge contains $50$ percent water by weight. This sludge is first centrifuged, and $0\mathrm{.}1$ kilograms of water are removed per kilogram of wet sludge feed. The sludge is dried further using air so that the final product contains $10$ percent by weight water. The air for drying is heated, passed into an oven drier, and vented back into the atmosphere. On a day when atmospheric pressure is $760mmHg,$ the temperature is $70F$ and the relative humidity is $50\%,$ calculate the cubic meters of wet air required to dry one kilogram of sludge fed to the process. The air vented from the oven drier is at $100F$ and $780mmHg.$ It has a dew point of $94F.$