Calculate the design-stage uncertainty in estimating a nominal pressure of 10,000 n/m^2 using an inclined manometer (resolution: 1 mm; zero error (offset) uncertainty: 0.5 mm) with water at 20℃ for inclination angles of 10 to 90 degree (using 20-degree increments). the inclination angle can be set to within 1 degree. the liquid used in the manometer has a specific weight of ym = 9,770 0.5% n/m^3 . the manometer resolution is 1 mm. zero-point offset error is 0.5 mm. also, in each of the three case (i. e., 10, 50, 90 degrees), determine which uncertainty element (i. e., the inclination angle, the specific weight of the liquid, or the length) dominates this the overall design-stage uncertainty.