Question

A solution of water and dissolved salt enters a cylindrical vessel with radius R. The volumetric inlet flow rate of solution in the vessel is q1 and the concentration of salt in the inlet is c1. The solution inside the vessel is kept well-stirred (assume perfect and instantaneous mixing, and constant density of the mixture) and flows out of the tank with flow rate q2 (see Figure 1).

Knowing that initially the vessel only contains pure water and that the initial level of water in the vessel is h0, determine c(t), the salt concentration in the vessel as function of time t, for the following cases:

q1 = q1(t), c1 = c1(t) and q2 = q2(t) are generic functions of time. In this case, only write the resulting differential equation for the dependent variable c(t). Since the actual expression of q1(t), c1(t) and q2(t) are unknown, the differential equation cannot be solved.

7it) c1(t) h(t) c(t) 920t)

Answer 1

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