Problem 8- Calibration and Sensitivity (10 points) The following data was taken

Question

Problem 8- Calibration and Sensitivity (10 points) The following data was taken from a pressure transducer - Pressure Output (Pa) 0.5 0.4 10 20 50 100 2.3 6.9 15.8 36.4 110.1 253.2 It has been plotted below- Pressure Transducer Calibration Curve 300 250 200 150 5 100 50 y 0.007x2+ 1.8556x-1.8307 80 100 120 02060 50 Pressure (Pa) Using the polynomial equation, estimate the sensitivity of the pressure transducer at a pressure of 50 Pa. a. Compare this sensitivity with that obtained by a linear fit through the endpoints of the data set. b.

Explanation / Answer

Solutiona;:

poynomial eq is

y=0.007x^2+1.8556x-1.8307

for x=50

y=0.007*50^2+1.8556*50-1.8307

y=108.4493

voltage =108.4493 volts for pressure =50 Pa

Solutionb:

sensitivity =110.1 V for pressure=50 Pa

predicted sensitivity=108.4493 V for pressure =50 Pa

Residual=predicted-observed

=108.4493-110.1

=-1.6507

A negative rsidual means the models prediction is too large(the model over estimates) the sensitivity for pressure=50 pa

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