f15_fall

f15_fall - Fluids Lecture 15 Notes 1. Uniform ow, Sources,...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Fluids Lecture 15 Notes 1. Uniform ow, Sources, Sinks, Doublets Reading: Anderson 3.9 3.12 Uniform Flow Definition V A uniform ow consists of a velocity field where vector = u + v is a constant. In 2-D, this velocity field is specified either by the freestream velocity components u , v , or by the freestream speed V and ow angle . u = u = V cos v = v = V sin 2 Note also that V 2 = u + v 2 . The corresponding potential and stream functions are ( x, y ) = u x + v y = V ( x cos + y sin ) ( x, y ) = u y v x = V ( y cos x sin ) V v u Zero Divergence A uniform ow is easily shown to have zero divergence vector u v V = + = 0 x y since both u and v are constants. The equivalent statement is that ( x, y ) satisfies Laplaces equation. 2 ( u x + v y ) 2 ( u x + v y ) 2 = + = 0 x 2 y 2 Therefore, the uniform ow satisfies mass conservation. Zero Curl A uniform ow is also easily shown to be irrotational, or to have zero vorticity . vector u V vector = v k = 0 x y 1 The equivalent irrotationality condition is that ( x, y ) satisfies Laplaces equation. 2 ( u y v x ) 2 ( u y v x ) 2 = + = 0 x 2 y 2 Source and Sink Definition A 2-D source is most clearly specified in polar coordinates. The radial and tangential velocity components are defined to be V r = , V = 0 2 r where is a scaling constant called the...
View Full Document

Page1 / 6

f15_fall - Fluids Lecture 15 Notes 1. Uniform ow, Sources,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online