The amount of salt Q in a well-stirred tank shown in Fig
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The amount of salt Q in a well-stirred tank shown in Figure E2.3 depends on c1, the concentration of salt in the brine s
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The amount of salt Q in a well-stirred tank shown in Figure E2.3 depends on c1, the concentration of salt in the brine solution entering the tank, as well as the flow rates F1 and F0 into and out of the tank. The continuous-time model is based on conservation of salt. It equates dQ=dt, the instantaneous rate of change in the amount of salt in the tank to the difference in the rate of salt entering the tank, c1F1, and the rate of salt flowing out of the tank, cF0. The tank initially contains 100 lb of salt-free water. The concentration of salt in the brine solution flowing in is 0.25 lb=ft3. Both the flow into and the flow out of the tank are both 1 ft3=min. Note that 1 ft3 of water weighs approximately 62.4 lb. (a) Find Q(t), the amount of salt in the tank as a function of time. (b) Find the amount of salt in the tank at steady state.
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