It is necessary to decrease the capacity of an existing distillation column by 30%. As a consequence, the amount of liquid condensed in the shell of the overhead condenser must decrease by the same amount (30%). In this condenser, cooling water (in tubes) is available at 30°C, and, under present operating conditions, exits the condenser at 40°C. The maximum allowable return temperature without a financial penalty assessed to your process is 45°C. Condensation takes place at 85°C.

If the limiting resistance is on the cooling water side, what is the maximum scale-down possible based on the condenser conditions without incurring a financial penalty? What is the new outlet temperature of cooling water? By what factor must the cooling water flow change?

Repeat Part (a) if the resistances are such that the cooling water heat transfer coefficient is three times the condensing heat transfer coefficient. You may assume that the value of the condensing heat transfer coefficient does not change appreciably from the design case. Does your solution exceed the maximum cooling water return temperature of 45°C? If so, can you suggest a way to decrease the condenser duty by 30% that would not violate the cooling water return temperature constraint?