Tuesday, December 27, 2011

MrsDrPoe: Blasius Boundary Layer Example

It's another Thesis Tuesday on the blog, and as promised, I'll be giving you an example of the Blasius Boundary Layer Solution.

Problem: A viscous fluid with a known density (rho = 1300 kg/m^3) flows past a flat plate such that the boundary layer thickness at a distance 1.3 m from the leading edge is 12 mm.  Determine the boundary layer thickenss, shear stress and friction coefficient at a distance of 0.2 m from the leading edge if the free stream velocity is 1.5 m/s.

Given: xk = 1.3 m, deltak = 12 mm, rho = 1300 kg/m^3, U = 1.5 m/s
Find: delta, tauw, and Cf at 0.2 m

Rek = (5*xk/deltak)^2 = 2.934x10^5

nu = U*xk/Rek = 6.646x10^-6 m*m/s
mu = nu*rho = 8.64x10^-3 N*s/m*m

Rex = U*x/nu =  45,140

delta = 5*x/sqrt(Rex) =4.707 mm

tauw = 0.3332*U^(3/2)*sqrt(rho*mu/x) = 4.571 Pa
Cf = 0.664/sqrt(Rex) = 3.125x10^-3

Pretty simple, huh?  Until next time...keep studying!


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