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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 – Gravity Force resultant du i dt Weight g dxdydz p xi g i Examples • Uniform linear acceleration: x3 du i dt xi du 3 p dt x1 0 p p x3 du 1 x3 g 3 g 3 p dt x1 du 1 p dt g i x1 g1 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 p x1 x1 0 0 a x1 x1 0 0 C 1 0 p g p x1 x1 g x1 a x1 g a x1 x1 C 1 a x g 7 1 x1 x g 0 . 7 x z 0 . 021 m Rotating flow • Rotation implies acceleration. du i dt p xi g i • Cylindrical coordinates are the most adequate • i.e. the parabola vertices is at z=0 and r=0. • The line along which p=p1 is: • At free surface p=p0 and thus: r 2 z surf 2 2g • i.e. the free surface is a parabola. Free surface formation • The volume above the resting level is equal to the volume below that level. • The free surface can cut the bottom. Curvilinear stream lines • Can we have any curvature? • We are limited by the pressure gradient. 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.