EXPERIMENT
RESPONSE
OF 1ST ORDER SYSTEMS IN INTERACTING TANKS
EXECUTIVE SUMMARY
The objective of this
experiment is to study the dynamic response of first order in interacting
tanks. To achieve the objective, the system was given a step change and an
impulse change at 40 and 50 LPH. Initially the system was subjected to step
function which was performed by two ways, i.e. giving a step-up from 40-50 LPH
and a step-down from 50-40 LPH. Followed
by impulse input at 40 and 50 LPH by adding 500 ml of water. , the height of
tank 2 suddenly increases and then decreases to achieve steady state. For
impulse change higher the flow rates more fluctuation and more time to achieve
steady state. The time constant for impulse change at different flow rate were
same so there was no effect on changing flow rate. For higher order, transfer
lag required is more and the system requires more time to achieve the ultimate
value. The resistance of the tank 2 is in the range of (r2) = 0.266
and time constant is in the range of (τ2) = 0.001772 sec.
1. OBJECTIVE:
To study the response of
two non- interacting tank system subjected to step and impulse change
2. THEORY:
The variation in h2 in tank
2 does not affect the transient response in tank1. This type of system is
called non interacting system.
Applying mass balance on
tank 1 and tank 2:
3. EXPERIMENTAL SETUP
 |
| Setup of interacting tank |
The setup consists of two
transparent body tanks with graduated scales connected in interacting mode by a
resistance pipe. While performing the interacting tanks experiment, the pipe
connecting tank 1 and tank 2 is kept completely closed. A rotameter with
flowrates in LPH is used for the supply. The outlet of the rotameter is used to
fill up the tank. A pump is present which recycles the water.
4. PROCEDURE:
1)
Start up the set up.
2)
A flexible pipe is provided at the rotameter outlet. Insert
the pipe in to the cover of the top Tank 1. Keep the outlet valves (R1 &
R2) of both Tank 1 & Tank 2 slightly closed. Ensure that the valve (R3)
between Tank 2 and Tank 3 is fully closed.
3)
Switch on the pump and adjust the flow at 70 LPH. Allow the
level of both the tanks (Tank 1 & tank 2) to reach at steady state and
record the initial flow and steady state levels of both tanks.
4)
Apply the step change with increasing the rotameter flow by @
10 LPH.
5)
Record the level of Tank 2 at the interval of 3 sec, until
the level reaches at steady state.
6)
Record final flow and steady state level of Tank1
7)
Repeat the experiment by throttling outlet valve (R1) to
change resistance.
Impulse change:
1)
Set the flowrate of tank at 50 LPH and allow it to achieve
steady state.
2)
Add 500 mL of water in tank 1 suddenly and start the
timer.
3)
Observe the change in height of tank 2 with respect to time
(sec) and note it down after every 3 sec until steady state is achieved and
stop the timer 4) Repeat the above steps for 60 LPH.
5)
Empty the tanks.
6)
Switch off the pump.
5. RESULTS AND DISCUSSION:
 |
| level of tank vs time for impulse change at 40 LPM |
The above figure shown the
level of tank vs time for impulse change at 40 LPM (~litre per minute). Level
of tank is representing on the y-axis and time for impulse change represented
on the x-axis.
It is dome in shape. The
height of tank 2 suddenly increases and then decreases to achieve steady state
value. Maximum height attained is 15 mm when flowrate is 40 LPH.
 |
| level of tank vs time for impulse change at 50 LPM |
It is dome in shape. The
height of tank 2 suddenly increases and then decreases to achieve steady state
value. Maximum height attained is 14 mm when flowrate is 50 LPH. The time to
achieve steady state at higher flow rate is higher for impulse change.
 |
| level of tank vs time for step change 40 LPM |
 |
| level of tank vs time for step change |
The above figure 4 and 5
epresents the response curve for interacting system subjected to step change.
Figure 3 is for step-up from 40 LPH where the height of the tank 2 increases
linearly with increase in time. Figure 4 is for step-down from 50 LPH where the
height of the tank decreases linearly with increase in time.
As the time increases the
level in the tank increase and achieve steady state. The resistance of the tank
2 is in the range of (r2) = 0.266 and time constant is in the range
of (τ2) = 0.001772 sec.
6. CONCLUSION
The aim is to study the
response of first order interacting system subjected to impulse and step
change. The height of tank 2 increases and decrease with time respectively. But
for impulse, the height of tank 2 suddenly increases and then decreases to
achieve steady state. For impulse change higher the flow rates more fluctuation
and more time to achieve steady state. The time constant for impulse change at
different flow rate were same so there was no effect on changing flow rate. For
higher order, transfer lag required is more and the system requires more time
to achieve the ultimate value. The resistance of the tank 2 is in the range of
(r2) = 0.266 and time constant is in the range of (τ2) =
0.001772 sec.
7. REFERENCES:
Coughanowr D., LeBlanc S., ‘Process Systems Analysis and Control’, Mc-Graw Hill Science Engineering
Math, 2nd Edition, 1991, Pg 228-238.
