Question #4

A system of three cylindrical tanks holding liquid is arranged as shown in Figure 1.

Fint

Fina

Tank #1

R₁

F₁

h₁

h3

h₂

h₁

F₁ = R₁

Tank #2

R₂

F₂

Tank #3

Figure 1- Schematic showing layout of tanks.

For all three tanks you can assume that the outlet flow rate is equal to the height in the tank divided by the

valve resistance, i.e.:

h3

hz

F₂= F3:

R₂

R3

a. Clearly derive the transfer function that relates the height in tank #1 (hi) to the inlet flow to the tank

(Fin).

[4 marks]

b. Tank #1 is 0.5 m in diameter and the value of R₁ is 200 s m². At steady state the liquid height is 1 m.

What is the flow rate of liquid entering the tank (i.c. what is Fin,1)?

[1 mark]

c. Calculate the gain and time constants for tank #1.

[2 marks]

d. Derive the transfer function that relates the height in tank # 3 (ha) to the flow entering the system (i.e.

to Flis and F2.in).

[5 marks]

c. Tank #2 has the same diameter as Tank #1, but R₂ = 0.5R₁. Tank #3 has double the diameter of Tank

#1 (i.e. it is 1 m in diameter), and R3= R₁. Fin1 = Fin2 = 0.01 m³ s¹. If the system is at steady state what

is the liquid level in each of the tanks?

[3 marks]