{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Problem 2.25 - Problem 2.25[Difficulty 3 Given Flow field...

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

View Full Document Right Arrow Icon
Problem 2.25 [Difficulty: 3] Given: Flow field Find: Pathline for particle starting at (3,1); Streamlines through same point at t = 1, 2, and 3 s Solution: For particle paths dx dt u = a x t = an d dy dt v = b = Separating variables and integrating dx x a t dt = or ln x ( ) 1 2 a t 2 c 1 + = dy b dt = or y b t c 2 + = Using initial condition (x,y) = (3,1) and the given values for a and b c 1 ln 3 m ( ) = an d c 2 1 m = The pathline is then x 3 e 0.05 t 2 = and y 4 t 1 + = For streamlines (at any time t) v u dy dx = b a x t = So, separating variables dy b a t dx x = Integrating
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}