Orifice Calibration:

Two Phase Small AirBY: JESSICA CATLIN, DYLAN HELM , AND YEN NGUYEN

Objective

Orifice Flow Calibration Future Experiments Develop Model

Flow Ranges (0-0.3 SCFM) a=0.0575, b=0.592

Testing

Equipment

Gas Flow Meter Zero and Range Screws

Control Valve

EHS&LP

Air

Leaks

Water in Line

Pressure Regulation

Data Model

Constant is unit conversion from (L/min) to (SCFM) 294.11= standard temperature (K) 101.3= standard pressure (kPa)

Process Model

Horizontal pipe, steady state, inviscid, and incompressible

Notice Standard Flow

Uncertainty

Variables with uncertainty

Expectations

Square root model

Unknown constant a is positive

Unknown constant b is close to 0.5

Average residual close to zero 0 2 4 6 8 10 120

0.5

1

1.5

2

2.5

3

3.5

Expected Plot of Q vs. (i-io)

i-io

Q

Experimental Plan

Open necessary valves

Set pressure regulators

Adjust zero () and range Flow must be turned off for zero

Attach the flow meter

Set valve at random operating %

Record the current (i)

Experimental Plan (cont.)

Measure (), 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

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= 0.057506788b= 0.59197892

Results

0 2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

0.25

0.3

0.35Q vs. (i-io)

ModelExperiment

(i-io)

Q

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 -15.50.072 4.280 108.8 294.5 0.084121084 -16.80.075 4.350 108.8 294.5 0.085496896 -14.00.083 4.940 109.3 294.5 0.097539227 -17.50.109 6.000 108.8 294.5 0.117926754 -8.20.105 5.910 108.8 294.5 0.116157852 -10.60.169 9.150 108.8 294.5 0.179838299 -6.40.176 8.700 108.8 294.5 0.170993793 2.80.166 8.41 108.8 294.5 0.165294 0.4

Statistical Test Results

Taken from Google Images

Statistical Test: Two-tailed t-test Null Hypothesis = 0r ̄

Alternative Hypothesis ≠r ̄ 0 Significance level α = 0.05 (95% confidence level )

Mean of Residuals ( )r ̄ 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)

0.50.5 < p-value < 1.0

1Degree of freedom (14) 0.692 0.0781 0

Discussion

2σ = 0.03

Propagation of UncertaintyεV1 (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

Conclusion

Unknown Errors

Volume Measurements

Longer Time Intervals

Operating Limits

Orifice Calibration: Two Phase Small AirJESSICA CATLIN, DYLAN HELM, AND YEN NGUYEN

Questions?