uranium exists naturally in groundwaterhowever if the concen

uranium exists naturally in groundwater,however if the concentration is too high then the water is unsafe to drink suppose a tank containing 2000 liters of groundwater has 100 mg of dissolved uranium in it this is above the safety limit of 0.03mg/l. to correct this, water with a uranium concertation of 0.01mg/l is pumped into the tank at rate of 12 l per minute.the water in the tank is well stirred and is pumped out of the tank at the rate of 12 litters per minute. suppose that the pump taking the water out of the tank is alfunctionning and that the water is being pumped out ofthe tank at arate of 5L per minte. if the capacity of the tank is 2500 liters. then calculate the amount of uranium in the tank whn the tank is full.

Solution

Given, water in tank = 2000 litres

Water in flow rate = 12 Litres/min

Water out flow rate = 5 Litres/min

Capacity of tank = 2500 litres

Thus, time required to full the tank = (2500-2000)/(12-5) = 500/7 min = 71.43 min

Now, during 71.43 minutes, total water in flow in the tank = 71.43 * 12 = 857.14 Litres

This 857.14 litres of water of Uranium concentration 0.01 mg/litres is mixed with water of 2000 litres of Uranium concentration 0.05 mg/litre (=100/2000 mg/l).

Thus effective concentration of Uranium in the tank when full = [(2000*0.05)+(857.14*0.01)] / (2000+857.14)

= 0.038 mg/litres