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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 te rica 11

Aulateórica 11

Rotação do tipocorposólido.

Princípios de Conservação

(massa, momentum e energia)

rotating fluid
Rotating Fluid

http://www.youtube.com/watch?v=gCZL3mZAQos&feature=related

http://www.youtube.com/watch?v=YNC2_vtNtyk

rota o do tipo corpo s lido
Rotação do tipocorposólido

Angular velocity:

Aceleration:

Pressure Gradient must balance the inertia force:

integra o da equa o
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
the free surface is a parabola
The free surface is a parabola
  • The position of the free surface can be found using volume conservation or knowing that:
the over elevation
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.
the tea cup paradox
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
conservation of momentum quantidade de movimento
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.