An air pressure is to be measured relative to atmosphere using an inclined manometer with a resolution of 1 mm and a zero-offset error of 0.5 mm. Oil, with a specific weight listed as V= 9770 +/- 0.5% N/m3 is to be used. 10 measurements of the inclination angle with a protractor give a mean value of theta= 30 degrees with a standard deviation of 1 degree. In addition, ten independent measurements of the meniscus of the inclined leg along the tube (L) give a mean value of 254 mm with a standard deviation of 2 mm. The air pressure relative to atmosphere is given by the following equation: delta P = L*V*sin(theta) .
a) Determine the expected value of delta P and the uncertainty in the result at 95% confidence.
b) Is it possible to reduce the uncertainty below 6 N/m2 using this system? Explain your reasoning.