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Aula teórica 11

Aula teórica 11. Rotação do tipo corpo sólido . Princípios de Conservação ( massa , momentum e energia ). Rotating Fluid. http://www.youtube.com/watch?v=gCZL3mZAQos&feature=related. http://www.youtube.com/watch?v=YNC2_vtNtyk. Rotação do tipo corpo sólido. Angular velocity:.

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Aula teórica 11

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  1. Aulateórica 11 Rotação do tipocorposólido. Princípios de Conservação (massa, momentum e energia)

  2. Rotating Fluid http://www.youtube.com/watch?v=gCZL3mZAQos&feature=related http://www.youtube.com/watch?v=YNC2_vtNtyk

  3. Rotação do tipocorposólido Angular velocity: Aceleration: Pressure Gradient must balance the inertia force:

  4. Integração da Equação • Integrating fist in r (in an horizontal plane) • Differentiating in “z” • Where p0 is the pressure at the free surface. In fact at r=0 and z=0

  5. The free surface is a parabola • The position of the free surface can be found using volume conservation or knowing that:

  6. The over-elevation • Applied to the point located on the glass surface, at the same vertical coordinate as the free surface at the rotation axis gives: • The over-elevation above the still level is h/2.

  7. The Tea Cup paradox • Is the effect that moves tea leaves laying on the cup bottom to the cup axis when one rotates the tea inside the cup, using a spoon. • This case differs from the “solid rotation” because the velocity of the tea on the cup bottom is zero. As a consequence the pressure gradient necessary for balancing the centrifugal force is higher at the surface and lower at the bottom. See details at http://en.wikipedia.org/wiki/Tea_leaf_paradox

  8. Conservation of momentum (Quantidade de movimento) • The force exerted by the jet on the ball is equal to the force exerted by the ball on the jet (contrary sign) and balances ball weight.

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