Theodore von Kármán in 1930 theorized that turbulentshear could be represented by τturb = ε du/dy, whereε= ρκ2y2|du/dy| is called the mixing-length eddy viscosityand κ ≈ 0.41 is Kármán’s dimensionless mixing-lengthconstant [2, 3]. Assuming that τturb ≈ τw near the wall,show that this expression can be integrated to yield thelogarithmic overlap la).
Theodore von Kármán in 1930 theorized that turbulentshear could be represented by τturb = ε du/dy, whereε= ρκ2y2|du/dy| is called the mixing-length eddy viscosityand κ ≈ 0.41 is Kármán’s dimensionless mixing-lengthconstant [2, 3]. Assuming that τturb ≈ τw near the wall,show that this expression can be integrated to yield thelogarithmic overlap la).
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter6: Forced Convection Over Exterior Surfaces
Section: Chapter Questions
Problem 6.34P
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Theodore von Kármán in 1930 theorized that turbulent
shear could be represented by τturb = ε du/dy, where
ε= ρκ2y2|du/dy| is called the mixing-length eddy viscosity
and κ ≈ 0.41 is Kármán’s dimensionless mixing-length
constant [2, 3]. Assuming that τturb ≈ τw near the wall,
show that this expression can be integrated to yield the
logarithmic overlap la).
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