# salt concentration

Feb 3rd, 2012
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The problem discusses in detail the concentration of salt solution as function of time. Initial the solution has volume of V0, flow rate into the tank is P, and out of tank is q, and the concentration of infilling solution is c, and assume that the solution inside the tank is uniform at all time. Find the concentration of the salt in the tank as a function of t. The document illustrates how to set up the differential equation and solve it in details.

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The problem discusses the concentration of salt solution as function of time. Initial the solution has volume of V0, flow rate into the tank is P, and out of tank is q, and the concentration of infilling solution is c, and assume that the solution inside the tank is uniform at all time. Find the concentration of the salt in the tank as a function of t. Let y(t) be the amount of salt in the tank at time t, V0 the initial volume of the solution in the tank, the flow rate into the tank is p and out of tank is q, and the concentration of infilling solution is c, then at t, the volume of the solution is , the amount of salt added to the tank is pc in unit time, and the amount of salt flowing out of the tank is . Then we have the differential equation for y: Assume the integration factor of the eq is U, multiply U to both sides of the equation, Because U is the integration factor

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