A farmer has a mixing tank of capacity 1200 liters which she half-filled with pure, fresh...

A farmer has a mixing tank of capacity 1200 liters which she half-filled with pure, fresh water. She pumps into the tank a concentrated liquid fertilizer (CLF) at rate 3 liters/minute, containing 1/3 ∼ 0.333 kg/liter of nitrate (a salt of nitric acid). In addition, she pours the dry powder fertilizer (DPF, the same chemical as a soluble powder) at rate 1/12 = 0.08333 kg/min in the tank; her aim is to get a right solution concentration 0.12kg/liter for the type of soil she has in her field. Unfortunately, the tank is leaking: when the farmer checks it after 90 min (that is, 1.5 hr) she finds the tank containing only 330 liters of solution. Assume the leak is at the bottom of the tank. Then:

(a) Determine the leakage w in liters/min.

(b) In what time would the tank become empty? Let N(t) be the amount of nitrate in the tank at time t.

(c) Write the InValProblem for N(t) and

(d) solve it, for t in min, N(t) in kg.

(e) Find the amount N(t) and the concentration c(t) of nitrate in the tank at time t = tcheck when the farmer checks the tank. Find out:

(f) how much of the CLF in liters and

(g) how much of the DPF in kg has been pumped/poured in the tank by the time t = tcheck she checks the tank. In absence of leakage: determine

(h) the time t = t ∗ when c(t) would be at the right l evel 0.12 and

(i) the volume V of the liquid solution in the tank at t = t ∗ .

Expert Solution

Colby Messinger answered 2 years ago

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