Problem 2.21 - Problem 2.21 [Difficulty: 3] Given: Eulerian...

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

View Full Document Right Arrow Icon
Problem 2.21 [Difficulty: 3] Given: Eulerian Velocity field Find: Lagrangian position function that was at point (1,1) at t = 0; expression for pathline; plot pathline and compare to streamlines through same point at the instants t = 0, 1 and 2s Solution: Governing equations: For pathlines (Lagrangian description) u p dx dt = v p dy dt = For streamlines v u dy dx = Assumption: 2D flow Hence for pathlines u p dx dt = A = A2 = m s v p dy dt = B t = B2 = m s 2 So, separating variables dx A dt = dy B t dt = Integrating xA t x 0 + = x 0 1 = m yB t 2 2 y 0 + = y 0 1 = m The Lagrangian description is xt () At x 0 + = yt () B t 2 2 y 0 + = Using given data xt () 2t 1 + = yt () 1 t 2 = The pathlines are given by combining the equations t xx 0 A = yB t 2 2 y 0 + = B xx 0 () 2 2A 2 y 0 + = Hence yx () y 0 B xx 0 () 2 2A 2 = or, using given data yx () 1 x1 () 2
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

Page1 / 2

Problem 2.21 - Problem 2.21 [Difficulty: 3] Given: Eulerian...

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

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