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Unformatted text preview: 1 Lecture 3 Bernouilli’s equation Bernouilli s equation. ACT: Aluminum and lead Two blocks of aluminum and lead with identical sizes are suspended from the ceiling with strings of different lengths and placed inside a bucket of water as shown. In which case is the buoyant force greater? A. Al B. Pb ceiling C. It’s the same for both Al The displaced volume (= volume of the block) is the same in both cases. Depth or object density do not play any role. Pb The different weight is compensated with a different tension in the strings. Work by pressure A As an element of fluid moves during a short interval dt , the ends move distances ds 1 and ds 2 . 1 1 2 2 dV Ads Ads = = dV dV If the fluid is incompressible, the volume should remain constant: A 1 A 2 v 1 v 2 ( ) 1 1 1 2 2 2 1 2 dW pAds p Ads p p dV = − = − Work by pressure during its motion: ρ 1 ρ 2 ds 2 ds 1 Kinetic and gravitational potential energy ( ) ( ) 2 2 2 1 1 1 2 2 dK dV v dV v ρ ρ = − Change in kinetic energy: Change in potential energy: ( ) 2 1 dU g dV y y ρ = − y: height of each element relative to some initial level (eg: floor) A 1 A 2 v 1 v 2 ρ 1 ρ 2 ds 2 ds 1 2 Bernouilli’s equation Putting everything together: ( ) ( ) ( ) ( ) 2 2 2 1 2 1 1 2 1 1 2 2 dV v dV v g dV y y p p dV ρ ρ ρ − + − = − ( ) other d K U dW + = 2 2 1 1 1 2 2 2 1 1 2 2 p v g y p v...
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This note was uploaded on 09/21/2011 for the course PHYS 222 taught by Professor Johnson during the Spring '07 term at Iowa State.
 Spring '07
 Johnson
 Physics, Force

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