Problem 4 (25 points)
A 40-degree inclined water manometer is to measure a gauge pressure of 5000 Pa in a system involving air. The differential length on the manometer is measured with an accuracy of 0.5 mm and a resolution of 1 mm. The density of air compared to the density of water is negligible. The specific weight of water is 9980 +/- 1% N/meter cube. The inclination angle is set within 0.5 degrees. Calculate the design stage uncertainty in the measurement of this pressure gauge.