Aula teórica 11 Rotação do tipo corpo sólido. Princípios de Conservação (massa, momentum e energia)

Rotating Fluid

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:

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 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

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.