The dynamic behavior of the liquid level h in the tank R 1 is investigated when the inlet volumetric flow rate F 1 is changing. Both tanks, R 1 and R 2 , are operated at atmospheric pressure. The...

The dynamic behavior of the liquid level h in the tank R₁
is investigated when the inlet volumetric flow rate F₁
is changing. Both tanks, R₁
and R₂, are operated at atmospheric pressure. The liquid emerging from tank R₁
is recycled through the tank R₂
with the pump P .The system of the two tanks is shown in Fig. 4.26.

(a) Based on the mass balance of the liquid in the tank R1 and the momentum balance for the liquid in the output pipe of the same tank, develop the dynamic model describing the relationship between the level h in the tank (output) of the R₁
and the inlet flow rate F₁
(input).

(b) Linearize the obtained model and compute the transfer function of the process with the same input-output variables, considering the system as a capacitive first order system.