A tank with a capacity of 500 gallons originally contains 200 gallons of water w

Question

A tank with a capacity of 500 gallons originally contains 200 gallons of water with 100 lbs of salt in the tank. Water containing a salt concentrartion of (1+0.5sint (lbs/gal)) flows into the tank at a rate of 3 gal/min, and the mixture in the tank flows out at the rate of 1 gal/min.

a) Derive in details the differential equation for the amount Q(t) of salt in the tank at any time t. Can you solve this equation? What is Q(0)?

b) Assuming you have Q(t), what is the concentration of salt when water begins to overflow?

Explanation / Answer

a) 3(1+0.5sint)/{6(1+0.5sint)-1}

Q(0) = 0.6 lbs/min

b) 0.6258 gal/min

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