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# Exam1_2010 - Determine the pres-sure difference between the...

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57:020 Mechanics of Fluids and Transport Fall 2010 EXAM1 October 4, 2010 1. A layer of water flows down an inclined fixed surface with the velocity profile shown in Fig. 1. Determine the shearing stress that the water exerts on the fixed surface for 𝑈𝑈 = 2 m/s and = 0.1 m. (Use µ = 1.12 × 10 -3 N s/m 2 for water) 2. The dam in Fig. 2 is a quarter-circle 50 m wide into the paper. Determine the horizontal and ver- tical components of hydrostatic force against the dam and the angle of the resultant force from the vertical. (Use γ = 9790 N/m 3 for water) Fig. 1 Fig. 2 3. Blood (SG = 1) flows with a velocity of 0.5 m/s in an artery. It then enters an aneurysm in the ar- tery (i.e., an area of weakened and stretched artery walls that cause a ballooning of the vessel as shown in Fig. 3) whose cross-sectional area is 1.8 times that of the artery. Determine the pres- sure difference between the blood in the aneurysm and that in the artery.
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Unformatted text preview: Determine the pres-sure difference between the blood in the aneurysm and that in the artery. Assume the flow is steady and inviscid. (Use ρ water = 999 Kg/m 3 ) 4. The velocity components for steady flow through the nozzle shown in Fig. 4 are ± = − ² ³ ℓ ⁄ and ´ = ² [1 + ( µ ℓ ⁄ )] , where ² and ℓ are constants. Determine the pressure gradient along the y-axis at point (2) when the fluid is water with ² = 1 m s ⁄ and ℓ = 0.1 m . Neglect viscous effects and use the Euler quation ∇¶ = −· ¸ − ¹ º , where gradient ∇ = » »³ ¼̂ + » »µ ½̂ , ¸ = ¸ ³ ¼̂ + ¸ µ ½̂ is the flow acceleration, and ¹ = −¹½̂ is the gravity. (Use = 999 Kg/m 3 for water) Fig. 3 Fig. 4...
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