Chapter 6 Differential Analysis of Flow
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Transcript of Chapter 6 Differential Analysis of Flow
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Chapter 6Differential Analysis of
FlowCE30460 - Fluid Mechanics
Diogo Bolster
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Chapter Goals Kinematics of given flow field Continuous Continuity Equation Navier-Stokes and Specific Solutions Concepts of Potential Flow
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Kinematics Recall Material Derivative (Lagrangian vs
Eulerian)
Acceleration of a fluid element
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Types of Motion Translation Linear Deformation Rotation Angular Deformation
Draw each of these for a rectangular initial element….
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Types of Motion
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Linear Motion and Deformation
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In 3 dimensions Volumetric Dilatation Rate
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Angular Motion and Deformation
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Vorticity (Rotation)
Counterclockwise rotation is positive (z component is component out of the page). Others, in x-y also exist
vorticity (zero => irrotational)
Related, rate of shearing strain
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Sample Problem 1
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Sample Problem 2
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Conservation of Mass
But now in the limit of zero volume (to obtain differential form)
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Forms of Continuity Equation
General Form
Steady
Incompressible
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Cylindrical Polar Coordinates
General Form
Steady
Incompressible
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Streamfunction For incompressible, plane two dimensional
flow we can define a streamfunction psi, such that
Quantifies the flow rate between two streamlines (lines of constant psi)
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In cylindrical polar coordinates
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Sample Problem 1
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Sample Problem 2