4-Practice Problems - Chapter 4 Flowing Fluids and Pressure...

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Chapter4 FlowingFluidsandPressure Variation Problem4.1 A g32 ow moves in the g123 -direction with a velocity of 10 m/s from 0 to 0.1 second and then reverses direction with the same speed from 0.1 to 0.2 second. Sketch the pathline starting from g123 =0 and the streakline with dye introduced at g123 =0 g61 Show the streamlines for the g31 rst time interval and the second time interval. Solution The pathline is the line traced out by a g32 uid particle released from the origin. The g32 uid particle g31 rst goes to g123 =1 g61 0 and then returns to the origin so the pathline is The streakline is the con g31 guration of the dye at the end of 0.2 second. During the g31 rst period, the dye forms a streak extending from the origin to g123 = 1 m. During the second period, the whole g31 eld moves to the left while dye continues to be injected. The g31 nal con g31 guration is a line extending from the origin to g123 = g3 1 m. The streamlines are represented by 19
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20 CHAPTER4. FLOWINGFLUIDSANDPRESSUREVARIATION
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21 Problem4.2 A piston is accelerating upward at a rate of 10 m/s 2 . A 50-cm-long water col- umn is above the piston. Determine the pressure at a distance of 20 cm below the water surface. Neglect viscous e g30 ects. Solution Since the water column is accelerating, Euler’s equation applies. Let the g99 -direction be coincident with elevation, that is, the g125 -direction. Euler’s equation becomes g3 g67 g67g125 ( g115 + g16g125 )= g29g100 g125 (1) Since pressure varies with g125 only, the left side of Euler’s equation becomes g3 g67 g67g125 ( g115 + g16g125 )= g3 μ g103g115 g103g125 + g16
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