Given the cylindrical tank in Figure 2 where a chemical reaction AkB is occurring with reaction rate given by SA=kcA. Assume that you are given cAin (the inlet concentration of species A ), Vin,r (the radius of the hole in the bottom of the tank) and u=2gh for the outlet velocity. You may assume that the concentration is uniform throughout the tank (perfect mixing). Also assume that the reaction does not result in a change in the molar volume of the mixture. Figure 2: Cross-section of a tank of length L. 1. (6 pts) Starting from our integral mole balance, show that dtdcA=AchVin(cAincA)kcA where Ac is the cross-sectional area of the tank. Hints: - Note that both cA and V are changing in time. - You will need to derive an equation for dtdV which you can substitute. Note that you need to show work that demonstrates that you can derive this (working backward from the answer won't get you too far). Otherwise you won't receive credit. 2. (8 pts) Determine cA(t) and h(t) given: a tank diameter of 0.25m and height of H=1m,cA(0)=0mol/m3, cAin=100mol/m3,k=1s1, a hole in the bottom with radius r=1.5cm, an inlet flow rate tank such that at steady state the tank is 75% full, and an initial liquid level of 10% and 90% the tank height. Plot the concentration of A, the moles of A and the height of the liquid in the tank over a 10-minute time period. Put the results for the two initial liquid levels on the same plot, but provide separate plots for cA(t),NA(t) and h(t). 3. (2 pts) For the numbers in part 2, determine the steady-state concentration of A. Hint: at steady state, dtdci=0. Given the cylindrical tank in Figure 2 where a chemical reaction AkB is occurring with reaction rate given by SA=kcA. Assume that you are given cAin (the inlet concentration of species A ), Vin,r (the radius of the hole in the bottom of the tank) and u=2gh for the outlet velocity. You may assume that the concentration is uniform throughout the tank (perfect mixing). Also assume that the reaction does not result in a change in the molar volume of the mixture. Figure 2: Cross-section of a tank of length L. 1. (6 pts) Starting from our integral mole balance, show that dtdcA=AchVin(cAincA)kcA where Ac is the cross-sectional area of the tank. Hints: - Note that both cA and V are changing in time. - You will need to derive an equation for dtdV which you can substitute. Note that you need to show work that demonstrates that you can derive this (working backward from the answer won't get you too far). Otherwise you won't receive credit. 2. (8 pts) Determine cA(t) and h(t) given: a tank diameter of 0.25m and height of H=1m,cA(0)=0mol/m3, cAin=100mol/m3,k=1s1, a hole in the bottom with radius r=1.5cm, an inlet flow rate tank such that at steady state the tank is 75% full, and an initial liquid level of 10% and 90% the tank height. Plot the concentration of A, the moles of A and the height of the liquid in the tank over a 10-minute time period. Put the results for the two initial liquid levels on the same plot, but provide separate plots for cA(t),NA(t) and h(t). 3. (2 pts) For the numbers in part 2, determine the steady-state concentration of A. Hint: at steady state, dtdci=0
