PHY183-Lecture45 - Review Fluid Flow"Ideal Fluid...

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April 14, 2006 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2006 Lecture 45 April 14, 2006 Physics for Scientists&Engineers 1 2 Review - Fluid Flow A 1 v 1 = A 2 v 2 p + ! gy + 1 2 ! v 2 = constant ! “Ideal Fluid” - Laminar (non-turbulent), incompressible, non-viscous, irrotational ! Continuity Equation: (incompressibility) ! Bernoulli Equation: (Conservation of Energy) April 14, 2006 Physics for Scientists&Engineers 1 3 Example: Draining a Bottle ! The picture below shows a large cylindrical bottle of cross sectional area A 1 = 0.10 m 2 ! We drain this bottle through a small hole of radius 7.4 mm, resulting in an area A 2 =1.7x10 -4 m 2. ! We videotaped this experiment and show one frame each 15 seconds ! The initial height of the fluid column (water with red food coloring) in the bottle above the opening was h 0 = 0.30 m April 14, 2006 Physics for Scientists&Engineers 1 4 Example: Draining a Bottle (2) Example: Draining a Bottle (2) ! Question: ! What is the volume flow rate at time h = h 0 = 0 .3 m? ! Answer: ! Start with Bernoulli’s Eqn: ! Both the top and the drain are open to the atmosphere and so are at the same pressure. ! We thus obtain: p + ! gy + 1 2 ! v 2 = constant ! gy 1 + 1 2 ! v 1 2 = ! gy 2 + 1 2 ! v 2 2
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April 14, 2006 Physics for Scientists&Engineers 1 5 Draining a Draining a Bottle (3) ! Canceling out the density and reordering: where h = y 1 - y 2 is the height of the fluid column ! The continuity equation A 1 v 1 = A 2 v 2 relates the two speeds v 1 and v 2 : ! Since A 2 / A 1 =0.0017 is very small, we can simplify
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