Modeling a Tank.

Proposed Problem 2.1) Develop a model for the tank presented in Fig. 2.3, but consider that the flow rate of water that leaves the tank (Qour, m/h) depends on the level of the water (h) inside the tank, in the way Qout=1+0.1h (m /h). This can be a real situation because as the column of water increases, the pressure on the exit point also increases, and consequently the exit flow rate becomes greater. Assuming that the initial volume of water inside the tank is equal to 10 m' and the cross-sectional area of this tank is equal to 1 m, the initial level of water (h) is 10 m, so in the beginning, the flow rate that leaves the tank (Qout) is equal to 2 m /h. In the beginning, the input flow rate is equal to 2 m/h, so the volume of water remains constant, in a steady- state regime. If for some reason the inflow rate varies from 2 to 3 m/h, develop a mathematical model to represent how the level of water inside the tank varies with time. Define the initial condition needed to solve the equation generated from the modeling m 3 m3/h Initial water volume= 10 m3 2 m/h