University of Florida
Department of Mechanical Engineering
Tank Discharge Lab
EML 4304C
Written by: Christian Schneider
Date: 11/6/2006
ABSTRACT
Tank discharge of air in a compression tank can be modeled using thermodynamic
equations if some assumptions are made about the process. In this experiment a
distinction between Isothermal and Isentropic process are required to get the pressure –
time relationship. The pressure and temperature of the air inside the tank were measured
over time for three different cases, these cases were varied by changing the diameter of
the outflow orifice. For each case the pressure and temperature were found to decrease
exponentially with time as predicted by the thermodynamic equations. When the
experiment has been completed is has been found that both the Isotropic and Isentropic
models of the fluid pressure are fairly accurate and almost identical to each other. From
the experiment it can be concluded that either of these models could be used to calculate
the pressure within the take to a reasonable margin.
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INTRODUCTION / OBJECTIVE
 Reinforce students with compressible flow concepts.
 Develop theoretical relationship of pressure with time in the tank as air discharges
from the tank through an orifice.
 Determine that whether the air in the tank can be modeled as an isothermal or
isentropic process.
TECHNICAL APPROACH (THEORY/ANALYSIS)
Because we are now working with a compressible fluid the equations for
incompressible flow can not longer be used and new equations must be generated
The density depends on the temperature and pressure of the fluids given by the
following equation
P
(1)  
RT
R  287 N  m
kg  K
There are two cases which will correspond to Isothermal and Isentropic cases.
Isothermal
P0  P0i  e C1t
C1 
 .6847  A*  C D  RT 0
V0
Isentropic
 1

P0   P0i 7  C 2 t 


C2 
7
0.1369  C D  A*  RT0i
1
V0 P07i
Where A* is the orifice area and V0 is the tank volume of 0.125 m^3. The
discharge port coefficient has been assumed to be equal to 0.6
2
RESULTS
It can be seen as a first observation that the tank discharge took a much longer
time for the smaller holes before stabilizing at a constant pressure. As the hole diameter
increased the time for discharge decreased.
The flattening of the graphs at the end of the time frame is due to the fact that the
pressure inside the tank is approaching the atmospheric pressure and the conditions for
choked flow break down.
Each comparison shows the measured pressure along with the pressure calculated
by the Isotropic and Isentropic equations. From these graphs we can see that the
measured pressure is always slightly higher than either the Isotropic or Isentropic
pressures.
1/8" Flow
450.00
400.00
350.00
Pressure
300.00
250.00
Measured Pressure
Isothermal
Isentropic
200.00
150.00
100.00
50.00
0.00
0.00E+00
2.00E+01
4.00E+01
6.00E+01
8.00E+01
1.00E+02
1.20E+02
1.40E+02
1.60E+02
Time
3
3/16" Flow
4.50E+02
4.00E+02
3.50E+02
Pressure
3.00E+02
2.50E+02
Measured Pressure
Isothermal
Isentropic
2.00E+02
1.50E+02
1.00E+02
5.00E+01
0.00E+00
0.00E+00
2.00E+01
4.00E+01
6.00E+01
8.00E+01
1.00E+02
1.20E+02
Time
3/32" Flow
4.50E+02
4.00E+02
3.50E+02
Pressure
3.00E+02
2.50E+02
Measured Pressure
Isothermal
Isentropic
1
2.00E+02
1.50E+02
1.00E+02
5.00E+01
0.00E+00
0.00E+00
5.00E+01
1.00E+02
1.50E+02
2.00E+02
2.50E+02
3.00E+02
3.50E+02
Time
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CONCLUSIONS
From the graphs which have been generated it can be seen that both the Isotropic
and Isentropic models give good approximations of the pressure versus time. As for
which of these gives the better approximation, it can be seen that both the models give
very similar estimates of the pressure, sometimes with one being more accurate than the
other but never by more than a few percent.
In this experiment there can be a great deal of error attributed to the measuring
devices which have been used. The pressure and temperature sensors which measure the
state of the air inside the tank have not been calibrated for this lab and their accuracy can
be called into question. Another large source of error is the diameter of the orifice. This
has been given to us by the instructor and needs to be assumed as accurate. Not only does
the diameter have to be called into question but also the smoothness of the orifice would
effect the flow rate and pattern of the gas from the tank. This would have a great effect on
the flow rate as the air exits the tank. These parameters would have to be measured and
quantified to be able to give an error estimate.
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