{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Problem 2.20

# Problem 2.20 - Problem 2.20[Difficulty 3 Given Velocity...

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

Problem 2.20 [Difficulty: 3] Given: Velocity field Find: Plot of pathline traced out by particle that passes through point (1,1) at t = 0; compare to streamlines through same point at the instants t = 0, 1 and 2s Solution: Governing equations: For pathlines u p dx dt = v p dy dt = For streamlines v u dy dx = Assumption: 2D flow Hence for pathlines u p dx dt = B x 1 A t + ( ) = A 0.5 1 s = B 1 1 s = v p dy dt = C y = C 1 1 s = So, separating variables dx x B 1 A t + ( ) dt = dy y C dt = Integrating ln x ( ) B t A t 2 2 + C 1 + = ln y ( ) C t C 2 + = y e C t C 2 + = e C 2 e C t = c 2 e C t = x e B t A t 2 2 + C 1 + = e C 1 e B t A t 2 2 + = c 1 e B t A t 2 2 + = The pathlines are x c 1 e B t A t 2 2 + = y c 2 e C t = Using given data x e B t A t 2 2 + = y e C t = For streamlines

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

View Full Document