Question

7 Water is flowing into the top of an open cylindrical tank (diameter D) at a volume flow rate of e and out of a hole in the bottom at a rate of O The tank is made of wood that is very porous and the water is leaking out through the wall uniformly at a rate of q per unit of wetted surface area. The initial depth of water in the tank is 2,. Derive an equation for the depth of water in the tank as a function of time. If Q, = IO gpm, Q, 5 gprn, D = 5 ft, q 0.1 gpm/ft, and z,-3 ft, is the level in the tank rising or falling?

Answer 1

We use the law of conservation of mass

Input = output + accumulation

Q1 is the input and Q0 plus the leakage is the output. Accumulation is varying as a function time.

So we can write the equation as follows -

miia) e a olt lion of time hi rhur valume of wate m tank A- wetied sutace area

2 2 2. し1 2
Thus the level is rising