p1122 - y and comparing to the equation for / y above, y =...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
28 CHAPTER 11. POTENTIAL FLOW 11.22 Chapter 11, Problem 22 Problem: Determine the velocity potential for a flow whose velocity vector is u = U [ i +( y/a ) j ] ,wh e r e U and a are constant velocity and length scales, respec- t ive ly .Isth isf lowincomp ress ib le? Solution: Since the velocity vector is u = U i + U ( y/a ) j , the velocity potential satisfies the following differential equations. u = ∂φ x = U and v = ∂φ y = U y a Integrating the first equation over x ,wef ind φ ( x, y )= Ux
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y and comparing to the equation for / y above, y = f I ( y ) = f I ( y ) = U y a = f ( y ) = Uy 2 2 a + constant Therefore, the velocity potential is ( x, y ) = U ^ x + y 2 2 a + constant The flow is incompressible if u vanishes. To check, u = u x + v y = x ( U ) + y w U y a W = U a W = 0 Thus, the flow is not incompressible ....
View Full Document

This note was uploaded on 02/09/2012 for the course AME 309 taught by Professor Phares during the Spring '06 term at USC.

Ask a homework question - tutors are online