Lecture-2a - APPH 4200 Physics of Fluids Cartesian Tensors...

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Unformatted text preview: APPH 4200 Physics of Fluids Cartesian Tensors (Ch. 2) September 8, 2011 • Last Lecture: Review • Example Fluid Flow Problems • Geometric Identities • Vector Calculus 1 Hydrostatics of a Sphere 2 Examples: Fluid Flow • • • • • • • Continuity (mass conservation) Euler equation (force and acceleration) Vorticity (∇×U, swirls!!) Bernoulli’s Principle (Lift and pressure) Visualizing flow (tracing lines…) Flow at corner Flow around cylinder 3 Fluid Continuity (Conservation of Mass) 4 Newton’s Law for a Fluid Element 5 Vorticity and Definitions 6 Bernoulli’s Principle 7 Visualizing Fluid Flow 8 Continuity, Vorticity, and Force 9 Flow at a Corner 10 Boundary Conditions 11 Solution Using Velocity Potential (and Streamlines) 12 Solution Using Streamfunction 13 What is the Pressure Along the Corner? 14 Rotating Cylinder http://www.grc.nasa.gov/WWW/K-12/airplane/cyl.html 15 Flow Around a Cylinder (See Ch. 6-9) 16 Velocity Potential Solution 17 What is the Pressure at the Surface of the Cylinder? 18 Equations for Incompressible and Irrotational Flow are Linear 19 A Solution with Circulation ϕ 20 Add Circulation to Flow 21 Summary • Continuity (incompressible flow and the Boussinesq approximation) • Force and acceleration (Euler equation) • Vorticity (∇×U, swirls!!) • Bernoulli’s Principle (Lift and pressure) • Visualizing flow (tracing lines…) • 2D Euler flow (inviscid) Important: B.P. can be used to find pressure from flow! 22 ...
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This document was uploaded on 10/18/2011.

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