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

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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

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Force resultant

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Examples Uniform linear acceleration: x1 x3

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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: x1 x3

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Rotating flow Rotation implies acceleration.

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Cylindrical coordinates are the most adequate

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

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

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

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

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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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