aula teórica 11
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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:. - PowerPoint PPT PresentationTRANSCRIPT
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:
Aceleration:
Pressure Gradient must balance the inertia force:
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 position of the free surface can be found using volume conservation or knowing that:
220 2
rgzpp
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:
g
Rh
rghpp
2
2
1
22
2200
• The over-elevation above the still level is h/2.
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)
• 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.