This document describes an orifice flow calibration experiment conducted by Jessica Catlin, Dylan Helm, and Yen Nguyen. The objective was to develop a model for air flow rates between 0-0.3 SCFM. Data was collected using various equipment and analyzed to determine constants a=0.0575 and b=0.592 for the model Q = a(i - io)b. Testing of the model found errors within ±15.5% and statistical analysis found the mean residual to be insignificant. Uncertainty analysis calculated average error to be 0.00941 SCFM. The document concludes there may be unknown errors from volume measurements and operating limits.

1. Orifice Calibration:
Two Phase Small Air
BY: JESSICA CATLIN, DYLAN HELM , AND YEN NGUYEN

2. Objective
 Orifice Flow Calibration
 Future Experiments
 Develop Model
 𝑄 = 𝑎(𝑖 − 𝑖 𝑜) 𝑏
 Flow Ranges (0-0.3 SCFM)
 a=0.0575, b=0.592
 Testing

3. Equipment
Gas Flow Meter Zero and Range Screws Control Valve

4. EHS&LP
 Air
 Leaks
 Water in Line
 Pressure Regulation

5. Data Model
 𝑄 𝑎 =
𝑉2−𝑉1
𝑡2−𝑡1
 𝑄𝑠 = (0.03531) ∗ 𝑄 𝑎 ∗ (
𝑇𝑠
𝑇
) ∗ (
𝑃
𝑃𝑠
)
 Constant is unit conversion from (L/min) to (SCFM)
 294.11= standard temperature (K)
 101.3= standard pressure (kPa)

6. Process Model
 𝑄 𝑎 = 𝐶 𝑜 𝐴 𝑜
2(∆𝑃)
𝜌(1−𝛽4)
 Horizontal pipe, steady state, inviscid, and incompressible
 𝑄𝑠 = 𝑎(𝑖 − 𝑖 𝑜) 𝑏
 Notice Standard Flow

7. Uncertainty
 Variables with uncertainty
 𝑉1, 𝑉2, 𝑡1, 𝑡2, 𝑃𝑎𝑡𝑚, 𝑃, 𝑇
𝜀 𝑄,95% =
𝑑𝑄
𝑑𝑉1
2
∗ 𝜀 𝑉1
2 +
𝑑𝑄
𝑑𝑉2
2
∗ 𝜀 𝑉2
2 +
𝑑𝑄
𝑑𝑡1
2
∗ 𝜀𝑡1
2 +
𝑑𝑄
𝑑𝑡2
2
∗ 𝜀𝑡2
2 +
𝑑𝑄
𝑑𝑃𝑎𝑡𝑚
2
∗ 𝜀 𝑃 𝑎𝑡𝑚
2 +
𝑑𝑄
𝑑𝑃
2
∗ 𝜀 𝑃
2 +
𝑑𝑄
𝑑𝑇
2
∗ 𝜀 𝑇
2

8. Expectations
 Square root model
 Unknown constant a is positive
 Unknown constant b is close to 0.5
 Average residual close to zero 0
0.5
1
1.5
2
2.5
3
3.5
0 2 4 6 8 10 12
Q
i-io
Expected Plot of Q vs. (i-io)

9. Experimental Plan
 Open necessary valves
 Set pressure regulators
 Adjust zero (𝑖 𝑜) and range
 Flow must be turned off for zero
 Attach the flow meter
 Set valve at random operating %
 Record the current (i)

10. Experimental Plan (cont.)
 Measure (𝑉2 − 𝑉1), T, and P
 1 minute interval
 Repeat fifteen times
 Plug data into spreadsheet
 Determine a and b using solver
 Plug model into NI LabVIEW
 Test the model
 9 trials

11. Data
Run Experimental Flow (Liters) Time (min) Actual Flow (L/min) Temperature (C) Pressure (kPa) Standard Flow (SCFM) Current (mA) i-io (mA) Modeled Flow Rate Q (ACFM) Squared Deviation
13 0.92 1 0.92 21.5 108.3 0.035 4 0.8 0.050 0.000246701
1 1.55 1 1.55 21 108.8 0.059 4.8 1.6 0.076 0.000294121
7 2.4 1 2.40 21.5 108.8 0.091 5.1 1.9 0.084 4.63685E-05
10 2.65 1 2.65 21.5 108.8 0.100 5.3 2.1 0.089 0.00012422
5 2.59 1 2.59 21.5 110.3 0.099 5.6 2.4 0.097 8.33137E-06
11 2.5 1 2.50 21.5 108.8 0.095 5.7 2.5 0.099 1.7948E-05
8 3.32 1 3.32 21.5 109.1 0.126 6 2.8 0.106 0.000412202
2 3.2 1 3.20 21.5 109.3 0.122 6.3 3.1 0.112 8.83274E-05
3 3.18 1 3.18 21.5 110.1 0.122 7.7 4.5 0.140 0.000331658
6 4.2 1 4.20 21.5 109.2 0.160 8.5 5.3 0.154 2.82703E-05
15 4.79 1 4.79 21.5 109.6 0.183 11 7.8 0.194 0.000126736
12 5.78 1 5.78 21.5 108.8 0.219 14.3 11.1 0.239 0.000406417
9 7.75 1 7.75 21.5 109 0.294 16.4 13.2 0.265 0.000850742
14 7.72 1 7.72 21.5 109.8 0.295 17.7 14.5 0.280 0.000225965
4 7.52 1 7.52 21.5 110.2 0.288 20.1 16.9 0.307 0.000329187
Sum of Squared Deviations 0.003537195
Solution:
a= 0.057506788
b= 0.59197892

12. Results
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 5 10 15 20
Q
(i-io)
Q vs. (i-io)
Model
Experiment
Data Model Testing
Q modeled
(SCFM)
Q measured (L/min)
Pressure
(KPa)
Temperature (K)
Q measured
(SCFM)
Percent Error
(%)
0.073 4.290 108.8 294.5 0.084317629 -15.5
0.072 4.280 108.8 294.5 0.084121084 -16.8
0.075 4.350 108.8 294.5 0.085496896 -14.0
0.083 4.940 109.3 294.5 0.097539227 -17.5
0.109 6.000 108.8 294.5 0.117926754 -8.2
0.105 5.910 108.8 294.5 0.116157852 -10.6
0.169 9.150 108.8 294.5 0.179838299 -6.4
0.176 8.700 108.8 294.5 0.170993793 2.8
0.166 8.41 108.8 294.5 0.165294 0.4

13. Statistical Test Results
Taken from Google Images
Statistical Test: Two-tailed t-test
Null Hypothesis r̄ = 0
Alternative Hypothesis r̄ ≠ 0
Significance level α = 0.05 (95% confidence level )
Mean of Residuals (r̄)
Sample Standard
Deviation (sr)
Number of random samples
(N)
Test Statistics
(t)
0.061217 0.0577 15 0.0781
Data from Student's t-Distribution Table
Two-tails (P-value) 0.5 0.5 < p-value < 1.0 1
Degree of freedom (14) 0.692 0.0781 0

14. Discussion
2σ = 0.03
Propagation of Uncertainty
εV1 (L) εV2 (L) εt1 (min) εt2 (min) εPatm (kPA) εPgage (kPA) εT (ᵒC)
0.2 0.2 0.016666667 0.016666667 1 1 1
dQ/dV1 dQ/dV2 dQ/dt1 dQ/dt2 dQ/dPatm dQ/dPgage dQ/dT Error (95%)
-0.0379 0.0379 0.0348 -0.0348 0.00032 0.00032 -0.00012 0.00860
-0.0381 0.0381 0.0591 -0.0591 0.00054 0.00054 -0.0002 0.00872
-0.0381 0.0381 0.0913 -0.0913 0.00084 0.00084 -0.00031 0.00884
-0.0381 0.0381 0.1008 -0.1008 0.00093 0.00093 -0.00034 0.00888
-0.0386 0.0386 0.0999 -0.0999 0.00091 0.00091 -0.00034 0.00899
-0.0381 0.0381 0.0951 -0.0951 0.00087 0.00087 -0.00032 0.00885
-0.0382 0.0382 0.1267 -0.1267 0.00116 0.00116 -0.00043 0.00906
-0.0382 0.0382 0.1223 -0.1223 0.00112 0.00112 -0.00042 0.00905
-0.0385 0.0385 0.1225 -0.1225 0.00111 0.00111 -0.00042 0.00911
-0.0382 0.0382 0.1604 -0.1604 0.00147 0.00147 -0.00054 0.00932
-0.0383 0.0383 0.1836 -0.1836 0.00168 0.00168 -0.00062 0.00954
-0.0381 0.0381 0.2199 -0.2199 0.00202 0.00202 -0.00075 0.00985
-0.0381 0.0381 0.2954 -0.2954 0.00271 0.00271 -0.001 0.01075
-0.0384 0.0384 0.2965 -0.2965 0.00270 0.00270 -0.00101 0.01080
-0.0385 0.0385 0.2898 -0.2898 0.00263 0.00263 -0.00098 0.01074
Average Error (95%) 0.00941

15. Conclusion
 Unknown Errors
 Volume Measurements
 Longer Time Intervals
 Operating Limits

16. Orifice Calibration:
Two Phase Small Air
JESSICA CATLIN, DYLAN HELM, AND YEN NGUYEN
Questions?