f06_sp

# f06_sp - vector integraldisplay Fluids Lecture 6 Notes 1....

This preview shows pages 1–2. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: vector integraldisplay Fluids Lecture 6 Notes 1. 3-D Vortex Filaments 2. Lifting-Line Theory Reading: Anderson 5.1 3-D Vortex Filaments General 3-D vortex A 2-D vortex, which we have examined previously, can be considered as a 3-D vortex which is straight and extending to . Its velocity field is V = V r = 0 V z = 0 (2-D vortex) 2 r In contrast, a general 3-D vortex can take any arbitrary shape. However, it is subject to the Helmholtz Vortex Theorems : 1) The strength of the vortex is constant all along its length 2) The vortex cannot end inside the fluid. It must either a) extend to , or b) end at a solid boundary, or c) form a closed loop. Proofs of these theorems are beyond scope here. However, they are easy to apply in flow modeling situations. 2-D Vortex 3-D Vortices The velocity field of a vortex of general shape is given by the Biot-Savart Law . d vector + vector r V ( x, y, z ) = (general 3-D vortex) 4 | vector r | 3 The integration is performed along the entire length of the vortex, with vector r extending from the point of integration to the field point x, y, z . The arc length element d vector points along the filament, in the direction of positive by right hand rule....
View Full Document

## This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

### Page1 / 4

f06_sp - vector integraldisplay Fluids Lecture 6 Notes 1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online