1. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 1 Pressure Transient Fourier Analysis Experiment by Student X Group Y ME 435L Winter 2007

2. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 2 Objectives Calibrate a strain gage pressure transducer and compare to manufacturer’s calibration data Study transient response pressure fluctuations generated by rapid release of water from a raised tank Create a computer generated curve fit of analog pressure transient curve using a Discrete Fourier Transform Compare physical system to computer generated model Find pressures at  t=120° and  t=180°

3. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 3 Background Theory Strain Gage Pressure Transducer –Strain gages bonded to diaphragm in Wheatstone Bridge configuration. –Pressure gradient causes deflection in diaphragm –Resistance in strain gages is proportional to diaphragm deflection

4. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 4 Background Theory Strain Gage Pressure Transducer (Continued) –Low mass and relative stiffness of diaphragm lead to a high natural frequency and quick response time –Well suited to transient measurements

5. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 5 Background Theory Fourier Analysis –Infinite expression of coefficients multiplied by sines and cosines to approximate a continuous, complex function Fourier Transform –Method for decomposition of a measured signal (y(t)) into its amplitude-frequency components –Discrete Fourier Transform (DFT) Approximation of the Fourier Transform for use with finite data sets –Fast Fourier Transform (FFT) Algorithm to compute DFT quickly Uses N log 2 N operations as opposed to N 2 in the DFT

6. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 6 Fourier Analysis Theory

7. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 7 Equipment Viatran Corp. Model 119 Pressure Transducer –FSO Range: 0-40” WCD –Static Sensitivity: K = 100.54 +/- 15.3% mVDC / in WCD Agilent Technologies HP34970A Data Acquisition / Switch Unit –Operating Range: 0-10 VDC –Bias Error: 0.0035% of Reading + 0.0005% of Range

8. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 8 Equipment Agilent Technologies HP35670A Dynamic Signal Analyzer –Range: 90 dB –Accuracy +/- 0.15dB Operational Amplifier Bridge Signal Conditioning board –Gain potentiometer set to obtain 0.993 VDC at 10” WCD –Gain, G=120

9. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 9 Equipment Water Supply Tank –Hole in bottom plugged by stopper Ruler –Accuracy +/- 0.0625” PC with LABVIEW installed

10. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 10 Pressure Transducer Calibration Curve

11. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 11 Uncertainty Analysis B SE = 0.04” WCDB LIN = 0.16” WCD B HYS = 0.08” WCDB REP = 0.004” WCD B ZB = 0.716” WCD

12. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 12 Fourier Analysis of Pressure Transient Curve

13. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 13 Fourier Analysis of Pressure Transient Curve

14. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 14 Fourier Analysis of Pressure Transient Curve P(t) = 2.986 + 11.936 sin (πt ) + 3.282 sin (2πt + 1.512) + 1.482 sin (3πt - 1.557) + 1.064 sin (4πt - 1.408) + 0.577 sin (5πt - 1.164) + 0.577 sin (6πt + 1.152) + 0.656 sin (7πt - 1.198) + 0.318 sin (8πt - 1.222) + 0.239 sin (9πt - 0.246) + 0.328 sin (10πt + 0.653) + 0.537 sin (11πt + 1.241) + 0.477 sin (12πt - 0.931) + 0.129 sin (13πt + 0.766) + 0.368 sin (14πt + 0.436) + 0.517 sin (15πt + 1.57) + 0.338 sin (16πt - 0.349) + 0.169 sin (17πt - 0.733) + 0.338 sin (18πt + 0.960) + 0.348 sin (19πt - 1.132) + 0.129 sin (20πt + 0.069) + 0.149 sin (21πt + 0.155) + 0.288 sin (22πt - 1.247) + 0.239 sin (23πt - 0.944) + 0.050 sin (24πt + 0.724) + 0.199 sin (25πt + 0.91) + 0.159 sin (26πt + 1.479) + 0.119 sin (27πt - 1.136) + 0.030 sin (28πt - 1.217) + 0.099 sin (29πt + 0.973) + 0.139 sin (30πt + 1.533) + 0.099 sin (31πt - 1.139) + 0.050 sin (32πt + 1.529) + 0.090 sin (33πt + 1.187) + 0.109 sin (34πt + 1.546) + 0.080 sin (35πt + 1.299) + 0.050 sin (36πt + 1.57) + 0.070 sin (37πt + 1.294) + 0.090 sin (38πt + 1.516) + 0.070 sin (39πt -1.391) + 0.050 sin (40πt -1.528) [in. WCD]

15. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 15 Fourier Analysis of Noise in Static Region

16. SAMPLE ONLY 10/31/06FOR ME 435L DEMOSTRATION PURPOSES ONLY 16 Fourier Analysis of Noise in Static Region P(t) = 0.039 + 0.149 sin (100πt ) + 0.020 sin (200πt - 0.233) + 0.030 sin (300πt - 1.238) + 0.189 sin (400πt + 1.477) + 0.010 sin (500πt - 0.406) + 0.020 sin (600πt - 0.098) + 0.109 sin (700πt + 0.871) + 0.030 sin (800πt + 1.216) + 0.010 sin (900πt + 1.431) + 0.010 sin (1000πt + 1.045) + 0.010 sin (1100πt - 1.161) + 0.010 sin (1200πt + 0.139)+ 0.040 sin (1300πt + 0.507) + 0.020 sin (1400πt + 0.314) + 0.020 sin (1500πt + 0.015)+ 0.020 sin (1600πt - 1.327) + 0.010 sin (1700πt + 1.121) + 0.010 sin (1800πt - 0.81) + 0.010 sin (1900πt + 0.458) + 0.010 sin (2000πt + 0.078) [in. WCD]