A cylindrical tank of cross sectional area, A, is being filled up in three stages where, qf = B*t + q* qe = q* for 0 t t1 qf = -B*t + q* qe = q*...

for t > t2

a. Show the mass balances for the system in all THREE time regimes.

b. Assuming that h(@t=0) = h0, solve for height as a function of time, h(t) = ?, for any time between 0 and t1.

c. Using the results from part (b), solve for height as a function of time, h(t) = ?, for any time between t1 and t2.

d. Using the results from part (c), solve for height as a function of time, h(t) = ?, for any time greater then t2.

If you were to add a proportional controller for problem #2 to target the height at h0, then write the THREE new mass balances the system. (NOTE: you do NOT need to solve these for height, just set up the mass balances with control)