1.2 The mass balance: exercise 2 (example)
A swimming pool in the backyard of Professor Hamersma is cleaned by adding a bottle of chlorine to the swimming pool. Too much chlorine in a swimming pool can be dangerous and professionals say that a concentration of 1.5 mg/L at most is still safe. Prof. Hamersma is quite stubborn this time and decides to use the chlorine by himself.
In this exercise we will calculate the concentration of cleaning product in the water over time.
The swimming pool we are looking at is 25 meters in length, 10 meters in width and 2 meters in depth. The water level is 20 cm below the terrace of the backyard, so the water level is 1.8 meters. On Sunday morning, the professor throws 1000 gram of the cleaning product (chlorine in tablet form) into the pool. Then, after the concentration of the product is the same everywhere in the water, the professor turns on the pumps to refresh the water.
The water level is 20 cm below the terrace at all times and fresh water (with no chlorine in it) is flowing in with Φv=0.006 m3/s. The water can flow out at the other side of the pool through a sink.
Now we want to describe the concentration of cleaning product over time by making a balance equation.
Of course, the first thing we need to do is to make a situation sketch. Remember that this is the most important step of the solving process!
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