Part 3: Well-type Manometer Some manometers are constructed as in shown in the figure below. where one side is a large reservoir (diameter D) and the other side is a small tube of diameter d, open to the atmosphere. This is called a well-type manometer. In such a case, the height of manometer liquid on the reservoir side does not change appreciably. This has the advantage that only one height needs to be measured rather than two, thus increase the sensitivity of the manometer. Sensitivity defined as the ratio of the manometer measured deflection h to the measured pressure in head unit. The manometer liquid has density p while the air has density p, Ignore the effects of surface tension. When there is no pressure difference across the manometer, the elevations on both sides are the same, as indicated by the dashed line. Height h is measured from the zero-pressure level as shown. (a) When a high pressure is applied to the left side, the manometer liquid in the large reservoir goes down, while that in the tube at the right goes up to conserve mass. Write an exact expression for p taking into account the movement of the surface of the reservoir. Your equation should give proze as a function of h, p and the physical parameters in the problem, h, d, D, and gravity constant g. (b) Write an approximate expression for pigage, neglecting the change in elevation of the surface of the reservoir liquid. (c) Suppose h = 0.26 m in a certain application. If pa = 101,000 Pa and the manometer liquid has a density of 820 kg/m²,estimate the ratio Dld required to keep the error of the approximation of part (b) within 1 percent of the exact measurement of part (a). |(d) Calculate and plot the error function of D/d ratio. (e) Igage What you suggest to increase the sensitivity of this type of manometers. Give an example that support your claim. To pressure measurement location Pa- Pa (air) Zero pressure level Pm P- Figure 4: Schematic for task 3 part 3.