Question

A tank having vertical sides and a bottom area of 100 ft² is used to store water. To fill the tank, water is pumped into the top at the rate given in the following table. Use Simulink to solve for and plot the water height h(t) for 0 ≤ t ≤10 min.

Answer 1

Consider the following data:

Area of the tank, A = 100 ft²

 

The relation between height h and the volume inflow rate q_i is expressed as,

A dh/dt = q_i

Where,

Time interval is t

Area of tank is A

Substitute 100 ft² for A in equation A dh/df = q_i.

100 dh/dt = q_i

Integrate both sides of the equation 100 dh/dt = q_i

h(t) = 1/100 ∫^t₀ qdt …… (1)

 

Given inlet flow rate q_i(ft³/sec) with time (minutes) is shown in the table below.

Table 1:

Time (min)	0	1	2	3	4	5	6	7	8	9	10
Flow rate	0	80	130	150	150	160	165	170	160	140	120
(ft3/sec)

 

The MATLAB m-file for solution of equation (1) is as follows:

t=[0:10];

q=[0,80,130,150,150,160,165,170,160,140,120];

for k=2:11,h(k)=(1/100)*trapz(t(1:k),q(1:k));

end

plot(t,h)

 

The plot obtained by MATLAB script written above is shown in Figure 1:

Figure 1

 

The height of water increases with time and final height achieved after 10 minutes is 13.65 ft.

Water height in the tank at time t = 10 min is 13.65ft.

The height of water increases with time and final height achieved after 10 minutes is 13.65 ft.

Water height in the tank at time t = 10 min is 13.65ft.