Search for question
Question

5. Some manometers are constructed as shown 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. The manometer liquid has density pm while the air has density pa. 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 Pigages taking into account the movement of the surface of the reservoir. Your equation should give Pigage as a function of h, pm, and the physical parameters in the problem, 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/m³, estimate the ratio D/d required to keep the error of the approximation of part (b) within 1 percent of the exact measurement of part (a).The error is defined as, \text { Error }=\frac{\Delta p_{\text {exact }}-\Delta p_{\text {approx }}}{\Delta p_{\text {exact }}} \text {. }

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6