A cylindrical tank of cross sectional area A1 contains liqui

A cylindrical tank of cross sectional area A1 contains liquid to a height h10 at time t0. Also at time t=0, a line connecting this tank to an empty cylindrical tank of cross sectional area A2 is opened and the first tank is allowed to drain into the second. Designate the height of the first and second tank by h1 and h2, respectively, and develop a mathematical model that relates h2 to A1, A2, h10, and t. Compute h2(t) when q1 depends on h as we showed in class,q =kh^(1/2).

Solution

Q the quantity of flow at any time relating the two cylinders are = A1h1 = A2h2 which is given in the class as q= kh^1/2

hence we have h2= A1 h1/A2 = kh1^1/2 /A2

So we have h2(t) = kh10(t)^1/2 /A2 As t increases, the h2 increases as function of h1