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Transcript
APPH 4200 Physics of Fluids Cartesian Tensors (Ch. 2) Lecture 2a • Last Lecture: Review • Example Fluid Flow Problems • Geometric Identities • Vector Calculus Hydrostatics of a Sphere of Earth Examples: Fluid Flow • • • Continuity (mass conservation) • • • • Bernoulli’s Principle (Lift and pressure) Euler equation (force and acceleration) Vorticity (∇×U, swirls!!) Visualizing flow (tracing lines…) Flow at corner Flow around cylinder Fluid Continuity (Conservation of Mass) Newton’s Law for a Fluid Element Vorticity and Definitions Bernoulli’s Principle Visualizing Fluid Flow Continuity, Vorticity, and Acceleration Constant Flow at a Corner Boundary Conditions Solution Using Velocity Potential (and Streamlines) Solution Using Streamfunction What is the Pressure Along the Corner? Rotating Cylinder http://www.grc.nasa.gov/WWW/K-12/airplane/cyl.html Flow Around a Cylinder (See Ch. 6-9) Velocity Potential Solution What is the Pressure at the Surface of the Cylinder? Equations for Incompressible and Irrotational Flow are Linear A Solution with Circulation ϕ Add Circulation to Flow 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!
