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Tutorial_Fluid Mechanics • Problem 1 Consider a U-tube whose arms are open to the atmosphere. Now water is poured into the U-tube from one arm, and light oil (ρ = 790 kg/m3) from the other. One arm contains 70-cm-high water, while the other arm contains both fluids with an oil-to-water height ratio of 6. Determine the height of each fluid in that arm. Water oil ha hw1 hw2 SAME FLUID, SAME LEVEL, SAME PRESSURE Problem 2 Freshwater and seawater flowing in parallel horizontal pipelines are connected to each other by a double U-tube manometer, as shown in Figure. hw = 60 cm; hhg = 10 cm; hair = 70 cm; hsea = 40 cm. Determine the pressure difference between the two pipelines. Take the density of seawater to be 1035 kg/m3. Can the air column be ignored in the analysis? Air hsea hair Sea water Fresh water hw hHg Mercury Problem 3 The gauge pressure of the air in the tank shown in Figure is measured to be 65 kPa. hw = 30 cm; hhg = h cm; hoil = 75 cm. ρoil = 720 kg/m3 and ρHg = 13,600 kg/m3. Determine the differential height h of the mercury column. 65 kPa Air hoil Water hw hHg Problem 4 The top part of a water tank is divided into two compartments as shown in Figure. Now a fluid with an unknown density is poured into one side, and the water level rises a certain amount on the other side to compensate for this effect. Based on the final fluid heights shown on the figure, determine the density of the fluid added. Assume the liquid does not mix with each other. Unknown fluid Water 80 cm 45 cm 50 cm Problem 5 Two chambers with the same fluid at their base are separated by a piston whose weight is 25 N, as shown in figure. Calculate the gauge pressures in chambers A and B. Pison A air air B D 50 cm 30 cm C 30 cm E water 90 cm 25 cm Problem 6 A gasoline line is connected to a pressure gauge through a double-U manometer, as shown in figure. If the reading of the pressure gauge is 370 kPa, determine the gauge pressure of the gasoline line. S.G. of gasoline = 0.7; S.G. of Hg = 13.6; S.G. of oil = 0.79 Pgage = 370 kPa Oil 45 cm Gasoline Pipe Air 22 cm 50 cm 10 cm Water Mercury Problem 7 A double inverted U-tube manometer containing oil (SG = 0.8), mercury (SG = 13.6) and water is used to measure large pressure difference between gas in pipe B and gasoline in pipe A as shown in figure. Knowing that h1 = 60 cm, h2 = 87 cm, h3 = 35 cm, and h4 = 24 cm, determine the presure difference between A and B. Neglect the gas density and use γwater = 9810 N/m3 for water.