The document describes an experiment to study the transient discharge of a pressurized tank through orifices of varying diameters, as well as a long tube, and compare the actual blowdown processes to an ideal isentropic process. An MKS pressure transducer and T-type thermocouple were calibrated. Pressure and temperature data were recorded during blowdown for each orifice/tube. The actual temperature decayed much more than the calculated isentropic temperature due to heat transfer. Discharge coefficients were calculated and ranged from 0.59 to 0.71, decreasing with smaller orifices/tubes due to friction.

1. 1
58:080 Experimental Engineering
Title:
Isentropic Blow-Down Process and Discharge Coefficient
Steven Cooke
Department of Mechanical Engineering
The University of Iowa
Iowa City, IA 52242
Submitted to:
Professor: Hongtao Ding
TA: Yuwei Li & Wei Li
Date Submitted:
Friday, November 8th
, 2013

2. 2
Abstract
The objective of the experiment was to study the transient discharge of a rigid pressurized
tank and coefficients for several different diameter orifices as well as a long tube comparing
actual blow down processes with an isentropic process for an ideal gas. Along with these
processes we were able to study the concept of choked flow. This was done through the
comparison of the experimental measurements and numerical model.
An MKS Baratron transducer was calibrated with a DAQ card by measuring the voltage
at different pressure levels. A T-type thermocouple was then calibrated using a thermistor as the
lab standard taking DAQ output readings at ambient room temperature and in an ice point cell.

3. 3
Table of Contents
Page
Introduction…………………………………………………………………………………… 4
Experimental Considerations……………………………………….................. ................... 4
Results and discussion………………………………………………………… ………….. 7
Conclusions and Recommendations………………………………………………………… 11
References…………………………………………………………………………………… 13
Appendix A:
Appendix B:
Appendix C:
Note: For List of Equipment please refer to experimental engineering lab notebook

4. 4
Introduction
The objective of the lab was to study the transient discharge of a rigid pressurized tank
and discharge coefficient (CD) for several different diameter orifices as well as a long tube, then
compare actual blow down processes with an isentropic process for an ideal gas. Also, from
these processes study and understand the concept of choked flow. This was done through the
comparison of the experimental measurements with the numerical model.
Choked flow is a limiting condition, which occurs when the mass flow rate will not
increase with a further decrease in the downstream pressure environment while upstream
pressure is fixed. This can be observed when upstream pressure is constant while downstream
pressure is reduced. Once gas flow doesn’t increase, the flow is considered choked. An
isentropic process is for the most part ideal in that no heat is added to the flow and none is lost
from friction. This means that the process is reversible and can be repeated with the same results
forwards and backwards. This relates to the discharge coefficient, which is the ratio of actual
discharge to the theoretical discharge coefficient, which is witnessed, in isentropic processes.
EXPERIMENTAL CONSIDERATIONS
The experimental setup to acquire the necessary data of the “isentropic” blow down tank
workstation included a pressure vessel, pressure transducers, a pressure gauge, an internal
thermocouple, and a computer assisted data acquisition system (Omega OMB-DAQ-3001 and
LabView 2012 software). Figure 1 shows the main components of the experiment. The Omega
absolute pressure transducer with a digital display was used as a standard to calibrate the MKS
Baratron pressure transducer, which was used to acquire the pressure data. A T-type

5. 5
thermocouple and the MKS Baratron transducer were connected to the DAQ to record the data.
The data acquisition is controlled with the software LabView 2012.
Figure 1 Apparatus for “isentropic” blow down process and discharge coefficient measurements
Figure 2 Schematic drawing for the pressure discharge experimental setup
In order to pressurize the tank, close the release valve and open the air line. Adjust the main
control valve until absolute pressure is read. When plugging in the DAQ card make sure to
insert the pressure transducer and thermocouple into channels 0 and 1 respectively. The leads
are plugged into the (+) 4 and (-) 5 to insure proper output.
Barometric pressure of the room was recorded and converted to be 14.77 psi. The
difference between the Omega absolute pressure transducer at atmospheric pressure and
Barometric pressure was recorded to be 0.47 psi. This difference was added to all future results
to “zero” the Omega transducer within its resolution so that it could be used as the lab standard.

6. 6
Calibration of an MKS Baratron transducer was carried out by measuring voltage output
from the DAQ card at 10 different pressure levels varying from 14 – 70 psi. The output voltages
for the DAQ card can be seen in Appendix A, Table 1. A 14.4-psi pressure was repeated 10
times in order to allow for repeatability error calculations in the error analysis section with raw
data in Table A.2.
Calibration of a T-type thermocouple was carried out with a thermistor as the standard.
DAQ card temperatures were read from the thermocouple while the thermistor read 24.94 C°.
Measurements were also taken in the ice point cell with standard of 0.21 C° read from the
thermistor. The data for both these readings can be seen in Appendix A, Tables 3 & 4
respectively.
Pressure and temperature decay were recorded during the blow-down process for orifice
restriction sizes of 0.035”, 0.028”, 0.021”, 0.0135” and a long tube of 1 mm opening. Using the
calibrated MKS Baratron transducer and internal T-type thermocouple the outputs were recorded
by the DAQ card by repeatidly pressurizing the tank to 70 psi and waiting for thermal
equilibrium. Once equilibrium was reached data recording began and the valve was opened
allowing pressure to release. Data was recorded until ambient pressure was reached. This was
done 5 times for each orifice making sure thermal equilibrium was reached before releasing the
pressure.

7. 7
RESULTS AND DISCUSSION
The calibration data was plotted and obtained the calibration curve shown in Figure 3
Figure 3 Calibration curve for MKS Baratron transducer
This revealed equation Equation 1:
Pressure [psi] = 19.473 ∙ Voltage [V] + 14.773 (1)
The error in the fit was calculated using Equation C1 which gives a final equation with
uncertainty of pressure [psi] = 19.473 ∙ voltage [V]+ 14.773 ± 0.0223. The repeatability
error was calculated by taking 10 readings at 14.4 psi. Using Equation C2 the repeatability error
was found to be 0.0002453 V or 0.0047789 psi. The accuracy of the instrument was then
calculated using Equations 2 & 3.
εcalibration = √εbias mean
2
+ εprecision
2
+ εresolution
2
+ εfit
2
(2)
Accuracy = 1 −
|εcalibration |
xtrue
(3)
Example calculations can be found in Appendix C with tabulated results in Table 1.

8. 8
Table 1 Calculated Accuracy and uncertainty for MKS Baratron transducer
Calibration data for the T-type thermocouple can be found in Appendix A, Tables 3 & 4. Using
the thermistor as a standard, the accuracy of the tank thermocouple at room temperature (was
calculated using Equations 2 & 3 above removing error in the fit and using data from Tables A.3
& A.4 for calculations. The ice point and ambient temperature errors for the thermocouple were
calculated using pooled statistics and the RSS.
Table 2 Calculated Accuracy and uncertainty for T-type thermocouple using pooled statics and RSS
Pressure and temperature decay for each orifice were then plotted in Figure 4.
Figure 4 Dimensionless pressure decay for each orifice in relation to time
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 50 100 150 200 250 300 350 400 450
Pressure(dimensionless)
Time (s)
Dimensionless Pressure Decay
#65
#70
#75
#80
Long Tube

9. 9
Note that the time for the dimensionless pressure to decay to one takes less time for the larger
orifices and more time for the smaller which makes sense logically from the equations. There is
a phenomenon witness by the long tube which has the largest diameter hole yet is between the
second smallest hole and the third smallest which can be explained by friction of the wall and
Equation 4.
𝜏 = 𝜇
𝜕𝑢
𝜕𝑦
(4)
Since pressure is the driving force for this process, the measured pressure in the isentropic
equation was used to calculate the corresponding ideal temperature for an isentropic process. By
using the measured pressure in the isentropic equation, the temperature for an isentropic process
undergoing the measured pressure change can be calculated. The equation relating the initial
(“1”) and final (“2”) states of an ideal gas undergoing an isentropic process is Equation 5.
𝑇2
𝑇1
= (
𝑃2
𝑃1
)
( 𝑘−1)/𝑘
(5)
Using the above equation in excel the comparison between experimental and isentropic processes
for each orifice were calculated and graphed which can be seen in Appendix B Figures B.1-B.5.
These show that there is a large difference in measured and isentropic process. Heat transfer is
very noticeable in the process and is witnessed by the large difference in the measured
temperature compared to the isentropic temperature, which is due to the friction caused by
molecules at the orifice. There is a noticeably larger difference for the Long tube orifice, which
is due to the extended time that the air has time to rub on the walls of the tube compared to
simply the orifice end for the limited amount of distance.
Calculation of the discharge coefficient was done in excel using Equation 6
t = [
Vtank
(√k∙R∙T0)∙CD∙Anozzle
] ∙ [
2
k−1
∙ (
k+1
2
)
k+1
2∙(k−1)
] ∙ [(
P0
Ptank
)
(k−1)
2∙k
− 1] (6)

10. 10
where,
t = the time from the start of the blow − down process
CD = the discharge coefficient
Vtank = the volume of the tank (3.769025 L)
R = gas constant for air (287 J/kg ∙ K)
k = specific heat ratio for air (1.4)
Anozzle = area of the nozzle (
Diameters are:65 → 0.035", 70 → 0.028",
75 → 0.021, #80→0.0135,long tube → 1 mm
)
T0 = starting temperature of process (K)
P0 = starting pressure of process
Ptank = tank pressure during process
Pstar = Pa ∙ 1.892929 = 99284.∙ 1.892929 = 187938.5 Pa (7)
Anozzle = π ∙
Dnozzle
2
4
= π ∙
8.89×10−4
4
= 6.207 × 10−7
m2
(8)
Tabulation of the calculated data for Equation 6 can be found in Table
Table 3 Tabulated data from excel calculations for each orifice
using the data from above the discharge coefficient can be calculated using Equation
CD = 8.64 ∙ Vtank ∙
[(
Po
Pstar
)
0.4
2.8
−1]
[tstar (√k∙R∙T0∙Anozzle )]
(9)
This equation is used along with Table 3 to find the discharge coefficients shown in Table 4

11. 11
Table 4 Discharge coefficients calculated in Excel
The uncertainty of these calculations can be calculated using Equation 9.
𝑢 𝐶 𝐷
= √(
𝜕 𝐶 𝐷
𝜕 𝑃0
∙ 𝑢 𝑃0
)
2
+ (
𝜕𝐶 𝐷
𝜕𝑇𝑠𝑡𝑎𝑟
∙ 𝑢 𝑇𝑠𝑡𝑎𝑟
)
2
+ (
𝜕𝐶 𝐷
𝜕 𝑇0
∙ 𝑢 𝑇0
)
2
(10)
The results are tabulated below in Table 4
Table 5 Tabulated results of total uncertainty for discharge coefficient calculations
CONCLUSION
The experimental process of this lab revealed that the smaller the orifice size the longer
the time to reach choked flow for the blow down process. For an isentropic process of an ideal
gas compared to the actual the temperature distribution is largely different because of friction.
Figure 5 Resulting discharge coefficients in relation to pressure ratio

12. 12
In future calculations for this lab I would recommend a better calibration process for the T-type
thermocouple because only two points were taken which was not enough to create a calibration
curve. Instead the uncertainty for these calculations were much larger than needed to be causing
added uncertainty.

13. 13
References
1. L.D. Chen, “Experimental Engineering Lecture Notes”,
http://www.engineering .uiowa.edu/~expeng/Lecture%20Notes/notes.pdf (1996).
2. Experimental Engineering course website,
http://www.engineering.uiowa.edu/~expeng/Labs/Labs_Refs/Lab%201c%20-
%20Example%20Calcs.pdf

14. 14
APPENDIX A: TABLES
Table A. 1 MKS Baratron calibration data
Table A. 2 Repeatability error data

15. 15
Table A. 3 Measured temperature of ambient air with standard of 24.94 C°
Table A. 4 Measured temperature in ice point cell with standard of 0.21 C°

16. 16
APPENDIX B: FIGURES
Figure B. 1 Comparison between experimental and isentropic process for 0.035” orifice
Figure B. 2 Comparison between experimental and isentropic process for 0.028” orifice
0
50
100
150
200
250
300
350
0
100
200
300
400
500
600
0 10 20 30 40 50 60 70 80 90
Pressurep,[kPa]
Time t, [s]
#65 - 0.035"
Measured Pressure
Isentropic Temperature
Measured Temperature
0
50
100
150
200
250
300
350
0
100
200
300
400
500
600
0 20 40 60 80 100 120 140
Pressurep,[kPa]
Time t, [s]
#70 - 0.028"
Measured Pressure
Measured Temperature
Measured Temperature

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Figure B. 3 Comparison between experimental and isentropic process for 0.021” orifice
Figure B. 4 Comparison between experimental and isentropic process for 0.035” orifice
0
50
100
150
200
250
300
350
0
100
200
300
400
500
600
0 50 100 150 200 250 300
Pressurep,[kPa]
Time t, [s]
#75 - 0.021"
Measured Pressure
Measured Temperature
Isentropic Temperature
0
50
100
150
200
250
300
350
0
100
200
300
400
500
600
0 50 100 150 200 250 300 350 400 450
Pressurep,[kPa]
Time t, [s]
#80 - 0.0135"
Measured Pressure
Measured Temperature
Isentropic Temperature

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Figure B. 5 Comparison between experimental and isentropic process for a tube with 0.039” orifice
0
50
100
150
200
250
300
350
0
100
200
300
400
500
600
0 20 40 60 80 100 120 140
Pressurep,[kPa]
Time t, [s]
Long Tube - 0.039"
Measured Pressure
Measured Temperature
Isentropic Temperature

19. 19
APPENDIX C: EXAMPLE CALCULATIONS
Equation C1:
ufit = syx = √
∑ (yi − yci)2n
i=1
ν
= √
0.00399
8
= 0.0223 psi
Equation C2:
urand = tv,95
S̅x
√N
= 2.228
0.0003482
√10
= 0.0002453 V
Equation C3:
𝑠 𝑥 = √
1
𝑁
∑ (𝑥 𝑖 − 𝑥)2𝑁
𝑖=1 = √
1
30
(1.978 × 10−6) = 0.0002568 V
Equation C4:
ubias = |x̅ − xtrue | = |14.3 − 14.77| = 0.47 psi
Equation C5:
ures =
resolution
2
=
0.1
2
= 0.05 psi
Equation C6:
uQ =
EFSR
2m
=
10
224
= 0.00059 V
Equation C7:
Accuracy = 1 −
|εcalibration|
xtrue
= 1 −
|0.47067|
14.77
= 96.81%