A cylindrical tank is used to store water for a town as shown in the figure belo

Question

A cylindrical tank is used to store water for a town as shown in the figure below. On any given day, the water supply inflow per day may fill the tank with an additional 6,7, or 8 ft of water. The daily demand or consumption of the water for the town will draw down the water level in the tank by an amount equivalent to 5, 6, or 7 ft of the water in the tank. 2. (a) What are the possible combinations of inflow and outflow of water in the tank in a given day? (b) If the water level in the tank is 7 ft from the bottom at the start of a day, what are the possible water levels in the tank at the end of the day? c) If the amounts of inflow and outflow of water for the tank are both equally likely, what would be the probability that there would be at least 9 ft of water remaining in the tank at the end of the day?

Explanation / Answer

(a)

The inflow will be 6,7 or 8 fts of the tank. The outflow would be 5,6,7 ft of water in the tank. Hence the possible inflow outflow combinations would be {(6,5),(6,6),(6,7),(7,5),(7,6),(7,7),(8,5),(8,6),(8,7)}

In the given set the first term is inflow and the second is the outflow.

(b)

(c)

Out of 9 equally possible secnarios depicted in the above table, 3 end up with 9 or more fts of water. Hence the required probability is ,

P = 3/9 = 1/3 = 0.3333

Serial Number (Inflow,Outflow) Change In water height Water level at end of day 1 (6,5) 1 8 2 (6,6) 0 7 3 (6,7) -1 6 4 (7,5) 2 9 5 (7,6) 1 8 6 (7,7) 0 7 7 (8,5) 3 10 8 (8,6) 2 9 9 (8,7) 1 8

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