Question 2 of 13: Percent Error in a Crosby Gauge Tester

Question 2: Percent Error in a Crosby Gauge Tester (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Find. The percent error in the gauge reading.

Approach. The dead-weight tester balances the known weight of the piston-and-weights stack against the oil pressure acting on the piston face; the pressure that balances that weight IS the true reference pressure, against which the gauge's own reading is compared.

1. Piston area. $$A = \frac{\pi}{4}D^2 = \frac{\pi}{4}(0.025)^2 = 4.909\times10^{-4}\ \text{m}^2$$
2. True pressure from the weight balance. At equilibrium the oil pressure force supports the weight of the piston and weights: $$p_{true} = \frac{mg}{A} = \frac{9(9.81)}{4.909\times10^{-4}} = 179\,863\ \text{Pa} = 179.86\ \text{kPa}$$
3. Percent error of the gauge under test. Comparing the gauge's indicated reading to this true reference value: $$\%\,\text{error} = \frac{p_{indicated}-p_{true}}{p_{true}}\times100 = \frac{179-179.86}{179.86}\times100 = \boxed{-0.48\%}$$