Transcription of Fluids – Lecture 15 Notes
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Fluids – Lecture 15 Notes
Fluids Lecture 15 Notes1. Uniform flow, Sources, Sinks, DoubletsReading: Anderson FlowDefinitionAuniform flowconsists of a velocity field where~V=u +v is a constant. In 2-D, thisvelocity field is specified either by the freestream velocitycomponentsu ,v , or by thefreestream speedV and flow angle .u=u =V cos v=v =V sin Note also thatV2 =u2 +v2 . The corresponding potential and stream functions are (x,y) =u x+v y=V (xcos +ysin ) (x,y) =u y v x=V (ycos xsin )Vvu Zero DivergenceA uniform flow is easily shown to havezero divergence ~V= u x+ v y= 0since bothu andv are constants. The equivalent statement is that (x,y) satisfiesLaplace s equation. 2 = 2(u x+v y) x2+ 2(u x+v y) y2= 0 Therefore, the uniform flow satisfies mass CurlA uniform flow is also easily shown to be irrotational, or to havezero vorticity.
Fluids – Lecture 15 Notes 1. Uniform flow, Sources, Sinks, Doublets Reading: Anderson 3.9 – 3.12 Uniform Flow Definition A uniform flow consists of a velocity field where V~ = uˆı+ v …
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