Figure 1 shows the schematic of two pools. Water is pumped into…

Figure 1 shows the schematic of two pools. Water is pumped into Pool 1 and the inlet flow rate can be manipulated. Pool 1 has a constant hold up (the volume of water in the pool is constant) and the outlet from the pool is through the overflow line. The overflow from Pool 1 goes to Pool 2. The outlet from Pool 2 is at its bottom and the output flow rate is proportional to the square root of the level of liquid in the pool with F2 =
sqrt(h2(t)). The cross sectional area of the Pool 2 is A2 = 10 ft2. Initially the pools are at a steady state with the inlet flow rate of Fi = 1 ft3/sec and a level of water in the second tank h2 = 1 ft.
Sam, a 2.5 ft tall boy, is standing in Pool 2 and the inlet flow rate to Pool 1 has been increased from 1 ft3/sec to 2 ft3/sec. Based on the above information do the followings.
Determine whether Sam will drown as a result of the change in the inlet flow rate in Pool 1?
If yes, how much time is available before Sam drowns?
If the cross-sectional area of Pool 2 was twice that of the current value, would Sam still drown? If yes, how much time would be available before Sam would drown?
Plot the level of water in the tank against time for the above two cases (i.e. A2 = 10 ft2 and A2 = 20 ft2 ).

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