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f11_fall - Fluids Lecture 11 Notes 1. Vorticity and Strain...

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Unformatted text preview: Fluids Lecture 11 Notes 1. Vorticity and Strain Rate 2. Circulation Reading: Anderson 2.12, 2.13 Vorticity and Strain Rate Fluid element behavior When previously examining uid motion, we considered only the changing position and velocity of a uid element. Now we will take a closer look, and examine the elements changing shape and orientation . Consider a moving uid element which is initially rectangular, as shown in the figure. If the velocity varies significantly across the extent of the element, its corners will not move in unison, and the element will rotate and become distorted. y V(y) V(y+dy) element at time t + t element at time t x z In general, the edges of the element can undergo some combination of tilting and stretching . For now we will consider only the tilting motions, because this has by far the greatest implications for aerodynamics. The figure below on the right shows two particular types of element-side tilting motions. If adjacent sides tilt equally and in the same direction, we have pure rotation . If the adjacent sides tilt equally and in opposite directions, we have pure shearing motion. Both of these motions have strong implications. The absense of rotation will lead to a great simplification in the equations of uid motion. Shearing together with uid viscosity produce shear stresses, which are responsible for phenomena like drag and ow separation. shear stresses, which are responsible for phenomena like drag and ow separation....
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f11_fall - Fluids Lecture 11 Notes 1. Vorticity and Strain...

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