Question

Pressure Problems The pictured U-tube is with the mercury open to the atmosphere at both ends. Assume that the mystery fluid does not mix with the Mercury (a) Let po represent atmospheric pressure, phg represent the density of mercury, and pi represent the density of the mystery fluid. Obtain an algebraic expression for the density of the mystery fluid in terms of some or all of the following: hi, ha, hs, and pe (b) For the situation shown in the figure, which is true, pr Phe Or Prhe Explain. If hi- 2.55 cm and h2 25.00 cm (clearly the figure is not to scale), then what is the most likely identity of the mystery fluid? On what scientific evidence did you base your choice? (c) Page 11 of 276 (d) If the absolute pressure at Point A is 114,200 Pa, what is the height hs? Use the nume from Part (c). Using previous numerical values, determine the gauge pressure at Point A. Take atmospheric pressure to be po 101,300 Pa. (e)

Answer 1

(a) The density of the mystery fluid, ρi, is given by the equation ρi = (h2 - h1) * ρHg. (b) In this situation, pρHg > pρi is true. This is because the density of mercury is greater than the density of the mystery fluid, so the pressure of the mercury is greater. The most likely identity of the mystery fluid is air, as this is the most common fluid found in the atmosphere. (c) The absolute pressure at Point A is calculated using the equation po + pρHg * h2 + pρi * hi. (d) Using the numerical values given, the height hs is calculated to be 2.55 cm. The gauge pressure at Point A can then be calculated to be 114,200 Pa - 101,300 Pa = 12,900 Pa. (e)