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Aula Teórica 6

Aula Teórica 6. Pressure distribution in “Rigid Body” type flows. What is a rigid body flow?. A flow is of the “Rigid body” if the adjacent elementary volumes maintain their relative position, i.e. if there is no shear. In this case forces are exclusively resulting from: Pressure or

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Aula Teórica 6

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  1. Aula Teórica 6 Pressure distribution in “Rigid Body” type flows.

  2. What is a rigid body flow? • A flow is of the “Rigid body” if the adjacent elementary volumes maintain their relative position, i.e. if there is no shear. • In this case forces are exclusively resulting from: • Pressure or • Gravity

  3. Force resultant

  4. Examples • Uniform linear acceleration: x3 x1

  5. If there is a free surface • The pressure is hydrostatic and consequently there is inclination…. • If acceleration is constant, the horizontal pressure gradient is constant and the free surface is a plane: x3 x1

  6. Rotating flow • Rotation implies acceleration.

  7. Cylindrical coordinates are the most adequate

  8. i.e. the parabola vertices is at z=0 and r=0.

  9. The line along which p=p1 is: • At free surface p=p0 and thus: • i.e. the free surface is a parabola.

  10. Free surface formation • The volume above the resting level is equal to the volume below that level. • The free surface can cut the bottom.

  11. Curvilinear stream lines • Can we have any curvature? • We are limited by the pressure gradient.

  12. Summary • If there is acceleration in a free surface flow, free surface inclination will appear. • If acceleration is linear and constant, the free surface is plan • If there is rotation at constant angular velocity, the free surface is a parabola.

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