# Evaporator Process Efficiency and Salt Concentration Calculation

## a. What is the ratio of water recovered to water fed in the series of evaporators?

Given that equal amounts of water evaporate in each of the evaporators and the brine leaving each evaporator is fed to the next one until the tenth evaporator.

## b. What is the weight fraction of salt leaving the fourth evaporator?

Considering that the brine coming out of the tenth evaporator contains 12% by weight of salt.

## a. Ratio of water recovered to water fed:

The ratio of water recovered to water fed in the series of evaporators is 1:512.

## b. Weight fraction of salt leaving the fourth evaporator:

The weight fraction of salt leaving the fourth evaporator is approximately 52.1%.

The evaporator process involves passing sea water containing 8.1% by weight of salt through a series of 10 evaporators. The objective is to recover fresh water by evaporating and condensing water, while concentrating the salt in the brine. In this specific scenario, equal amounts of water evaporate in each evaporator, and the brine leaving each evaporator is fed to the next one except for the tenth evaporator.

The ratio of water recovered to water fed can be calculated by considering the doubling of salt concentration in the brine with each evaporator. Since equal amounts of water evaporate in each stage, the ratio of water recovered to water fed is 1:2^(10-1) or 1:512.

To determine the weight fraction of salt leaving the fourth evaporator, we consider the cumulative concentration of salt in the brine. Each evaporator doubles the concentration of salt, so the weight fraction of salt leaving the fourth evaporator is 8.1% x 2^4, which equals approximately 52.1%.

Understanding these calculations is crucial for optimizing the efficiency of evaporator processes and managing salt concentration levels effectively. For further insights on evaporators, you can explore related resources and information.