# 2. Consider an open-top, well-mixed tank. At time = 0 s, the…

2. Consider an open-top, well-mixed tank. At time = 0 s, the contents are drained by gravity through a circular hole at the bottom with area A1 = 0.1 m2 . Also at time = 0 s, a stream containing species A at a concentration CA0 = 10 mol/m3 is pumped into the top of the tank at a constant flow rate Fin = 0.8 m3 /s. The tank has a cross-sectional area A2 = 10 m2 and is initially filled with water at a height h = 5 m. The initial concentration of species A in the tank is 0 mol/m3.
a. Perform an overall mass balance on the liquid contents of the tank to derive an equation for dh/dt, the rate of change of the liquid level, as a function of Fin, A2, A1, h, and g (the gravitational constant). Assume that the velocity of the liquid level in the tank (v2) is significantly less than the exit velocity of the fluid through the drainage hole (v1). Assume that the density of the liquid is constant and unaffected by the mixing of species A.
b. Solve the differential equation in part a and plot h as a function of time over the interval 0 < t < 600 seconds. c. Perform a mass balance on species A to derive an equation for dCA/dt as a function of Fin, A2, A1, h, g, CA and CA0. Solve this differential equation and plot CA as a function of time over the interval 0 < t < 600 seconds. Also plot the total moles in the system (V*CA or A2*h*CA) in a separate plot, using the same time interval. d. Is the assumption v1 >>> v2 valid? Justify your answer.