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## Q. 5.3

RECTANGULAR PULSE RESPONSE OF THE LIQUID LEVEL SYSTEM.

Let us return once again to the system of Example 5.1. The flowrate is again to be changed suddenly to 87 liters/min (0.087 m² /min), but this time we hold it at this value only for 2.5 min; returning it to its initial value of 37 liters/min (0.037 m³ /min).

What is the maximum value the liquid level will attain during the course of this experiment?

## Verified Solution

The expression for the peak value attained by a first-order system in response to a rectangular pulse input of magnitude A and duration b is given by:

$y_{max} = y(b) = AK(1 – e^{-b/ \tau})$

(Note that this expression is in terms of deviations from the initial steady-state value for the liquid level.)

Since in this example, A = 0.05, b = 2.5, and from Example 5.1 we recall that K = 10, $\tau$ = 2.5, with an initial liquid level of 0.37 m, the peak value for the liquid level is obtained from:

$h_{max} = 0.37 + 0.5 (1 – e^{-1})$

or

$h_{max} = 0.686 m$