Design of A Liquid Level Control System Lab Report

DescriptionLab 3
Design of a Liquid Level Control System
Introduction
In this lab you will model the level of liquid in a cylindrical container and design a controller to
maintain the liquid level at a specific height. Liquid level control is used in petrochemical industries
in re-boilers, waste water treatment plants, bioreactors etc. The output variable of interest is the
height of the liquid column in the container. The container can be spherical, cylindrical or any
other shape depending on the application. In our model, we consider the cylindrical case. Refer
to Figure 1, the input is a constant flow of liquid into the container through Fin by keeping the
valve (valve 1) open at all times. The controlled variable is the outflow of liquid from the container,
which depends on the position of the valve at Fout ; we will call this valve 2. Other applications of
this system may have Fin as the control and Fout fixed. The position is controlled by controlling
the speed at which valve 2 is opened and closed.
Figure 1: Schematic of liquid level control experiment
Bernoulli’s principle states that the sum of all mechanical energies in a fluid along a streamline
is the same at all points on that streamline. Equation 1 puts this in writing.
1
P + ρv 2 + ρgh
2
(1)
Where, P is pressure, ρ is density of fluid, g is acceleration due to gravity, v is velocity and h is the
fluid level. The inlet conditions are as in equation 2 and equation 3 which dictate that the volume
of a fluid is constant under incompressible flow
Ai ḣi = Fin − Fout
(2)
Ai v i = Ao v o
(3)
1
Then from Bernoulli’s principle, equating input and output at the junction of the bottom of the
tank and the outflow pipe, we have
1
1
Pi + ρvi2 + ρghi = Po + ρvo2 + ρgho
(4)
2
2
However, Pi = Po , ho = 0 and if the area of the inlet pipe is much greater than that of the outlet
pipe, Ai >> Ao then we have vi
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