2008_Exam1 - 12 for a rectangle with base and height )...

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57:020 Mechanics of Fluids and Transport Fall 2008 EXAM #1 October 6, 2008 1. A 25-mm-diameter ( ܦ ) shaft is pulled through a cylindrical bearing ( ܮ = 0.5 m) as shown in Fig. 1. The lubricant that fills the 0.3-mm gap ( ߜ ) between the shaft and bearing is an oil having a ki- nematic viscosity of 8.0 × 10 -4 m 2 /s and a specific gravity of 0.91. Determine the force ܲ re- quired to pull the shaft at a velocity ܷ of 3 m/s. Assume the velocity distribution in the gap is li- near (See sketch below). 2. A homogeneous, 4-ft-wide, 8-ft-long rectangular gate weighing 800 lb is held in place by a hori- zontal flexible cable as shown in Fig. 2. Water acts against the gate which is hinged at point ܣ . Friction in the hinge is negligible. Determine the tension, ܶ , in the cable. (Hint: ߛ = 62.4 lb/ft 3 for water; ܫ ௫௖ = ܾܽ
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Unformatted text preview: 12 for a rectangle with base and height ) Figure 1 Figure 2 3. The specific gravity of the manometer fluid shown in Fig. 3 is 1.07. Determine the volume flow rate, , if the flow is inviscid and incompressible and the flowing fluid is gasoline. (Hint: = 9.80 kN/m 3 ; = 6.67 kN/m 3 ) 4. Consider a sphere of radius = 1m immersed in a uniform stream = 1 m/s, as shown in Fig. 4. According to a theory, the fluid velocity along streamline is given by 1 / Find the fluid acceleration at = 2 . Figure 3 Figure 4 Hint) = : Shear stress = : contact area @ = 1000 Kg/m 3...
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