Thermodynamics

48 | Thermodynamics1–106 The lower half of a 10-m-high cylindrical containeris filled with water (r 1000 kg/m 3 ) and the upper half withoil that has a specific gravity of 0.85. Determine the pressuredifference between the top and bottom of the cylinder.Answer: 90.7 kPa1–109 A glass tube is attached to a water pipe, as shown inFig. P1–109. If the water pressure at the bottom of the tubeis 115 kPa and the local atmospheric pressure is 92 kPa,determine how high the water will rise in the tube, in m.Take the density of water to be 1000 kg/m 3 .OILSG = 0.85h = 10 mP atm = 92 kPaWATERρ = 1000 kg/m 3h = ?FIGURE P1–1061–107 A vertical, frictionless piston–cylinder device containsa gas at 250 kPa absolute pressure. The atmospheric pressureoutside is 100 kPa, and the piston area is 30 cm 2 . Determine themass of the piston.1–108 A pressure cooker cooks a lot faster than an ordinarypan by maintaining a higher pressure and temperature inside.The lid of a pressure cooker is well sealed, and steam canescape only through an opening in the middle of the lid. Aseparate metal piece, the petcock, sits on top of this openingand prevents steam from escaping until the pressure forceovercomes the weight of the petcock. The periodic escape ofthe steam in this manner prevents any potentially dangerouspressure buildup and keeps the pressure inside at a constantvalue. Determine the mass of the petcock of a pressurecooker whose operation pressure is 100 kPa gage and has anopening cross-sectional area of 4 mm 2 . Assume an atmosphericpressure of 101 kPa, and draw the free-body diagramof the petcock. Answer: 40.8 gP atm = 101 kPaPetcockA = 4 mm 2WaterFIGURE P1–1091–110 The average atmospheric pressure on earth isapproximated as a function of altitude by the relation P atm 101.325 (1 0.02256z) 5.256 , where P atm is the atmosphericpressure in kPa and z is the altitude in km with z 0 at sealevel. Determine the approximate atmospheric pressures atAtlanta (z 306 m), Denver (z 1610 m), Mexico City (z 2309 m), and the top of Mount Everest (z 8848 m).1–111 When measuring small pressure differences with amanometer, often one arm of the manometer is inclined toimprove the accuracy of reading. (The pressure difference isstill proportional to the vertical distance and not the actuallength of the fluid along the tube.) The air pressure in a circularduct is to be measured using a manometer whose openarm is inclined 35° from the horizontal, as shown in Fig.P1–111. The density of the liquid in the manometer is 0.81kg/L, and the vertical distance between the fluid levels in thetwo arms of the manometer is 8 cm. Determine the gagepressure of air in the duct and the length of the fluid columnin the inclined arm above the fluid level in the vertical arm.DuctAirL8 cmPRESSURECOOKER35°FIGURE P1–111FIGURE P1–108