The flow out of the tank shown in Figure is given by F 0 =cH 1/2 . The cross-sectional area of the..

The flow out of the tank shown in Figure is given by F0=cH1/2.
The cross-sectional area of the tank A=50 ft2 and the constant c=2ft3/min
per ft1/2. The tank is 25 ft in height and the initial level in the
tank H(0)= 6 ft.

                                                  

a.       The
flow into the tank
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 The flow out of the tank shown in Figure is given by F0=cH1/2.
The cross-sectional area of the tank A=50 ft2 and the constant c=2ft3/min
per ft1/2. The tank is 25 ft in height and the initial level in the
tank H(0)= 6 ft.

                                                  

a.       The
flow into the tank is F t F1(t)=1=10 ft3/min,
t_0. Find the steady-state height of liquid in the tank, H(_).

b.      Use
forward Euler integration with a suitable step size and compare  to the result from part (a).

c.       The
flow into the tank is F1(t)=4+(t/10) t_0. Use forward Euler
integration with a step size T and find the difference equation for updating the
state HA(n). Leave your answer in terms of c, A, and T.

d.      For
the input flow rate in part (c), using forward Euler integration with T=0.1
min, find nf, where nfT is the time required to fill the
tank, i.e., HA (nf-1)<25 and="">A (nf)_25.
Plot the results.

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