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?