A hot-wire anemometry system probe inserted into a wind tunnel is used to measur

Question

A hot-wire anemometry system probe inserted into a wind tunnel is used to measure the tunnel's centerline velocity, U. The output of the system is a voltage, E. During a calibration of this probe, the data listed in below was acquired. Assume that the uncertainty in the voltage measurement is 2% of the indicated value. Using a linear least-squares regression analysis determine the best fit values of A and B in the relation E^2=A+B*U^0.5. Finally, plot the fit with 95% confidence intervals and data with error bars as voltage versus velocity. Is the assumed relation appropriate?

Velocity(m/s)                                    Voltage 0.00                       3.19 3.05                       3.99 6.10                       4.30 9.14                       4.48 12.20                       4.65

Explanation / Answer

Sol)

The Regression model is y=a+bx

From Excel output

The Regreeion model is y=3.44+0.112 (Velocity)

And also 95% CI for Velocity is (0.035,0.188)

SUMMARY OUTPUT Regression Statistics Multiple R 0.936897 R Square 0.877775 Adjusted R Square 0.837033 Standard Error 0.232314 Observations 5 ANOVA df SS MS F Significance F Regression 1 1.162771 1.162771 21.54491 0.018848 Residual 3 0.161909 0.05397 Total 4 1.32468 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 3.440012 0.179949 19.11656 0.000313 2.867333 4.012691 2.867333 4.012691 Velocity 0.111838 0.024094 4.64165 0.018848 0.035159 0.188517 0.035159 0.188517

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