I'm attempting to find the highest free stream velocity over a flat plat before a sensor placed 'delta' away from it experiences turbulent flow. When I plot this in Matlab it seems that the turbulent boundary layer thickness decreases with velocity. This seems pretty counter intuitive to me, am I thinking of this in the wrong way? Or am I making a silly coding error?

These are the governing equations

$$\begin{align} \delta &\approx \dfrac{0.37x}{Re_x^{1/5}} \\ Re_x &= \dfrac{\rho u_0x}{\mu} \end{align}$$ Source

EDIT : Do not include any 'clear' or 'delete' code when posting, because many people do not want their workspace cleared.

Matlab Code

% clc
% clear all
rho = 1025;   % density of water
mu = 0.00108; % dynamic viscosity
x = 65e-3;    % distance from leading plate edge
U = linspace(0,10); % Free Stream Velocity
Re = (rho*U *x)/mu;
turb_lay = (0.382*x)./(Re).^0.2
lam_lay = (5*x)./(Re).^.5
xlabel('Velocity (m/s)')
ylabel('Boundary Layer Height (m)')
legend('Laminar Boundary', 'Turbulent Boundary')
  • 1
    $\begingroup$ Why would you think the boundary layer height increases with velocity? You even have the expression for $\delta/x \sim 1/U^{1/5}$. Hence, the boundary layer height decreases by $1/U^{1/5}$. $\endgroup$ – TRF Jan 5 '17 at 19:11
  • $\begingroup$ Poor intuition I suppose. I guess the quicker the flow is moving the less opportunity it has to spread outward from the plate and deform. $\endgroup$ – Dougb Jan 5 '17 at 23:03

As the velocity increases, the fluid will not be able to form a cohesive boundary layer because the fluid particles will not have the needed residence time near the boundary layer to add to it.


It would appear that your setup is OK. I would recommend reading a few documents or texts which discuss boundary layer behavior.

I found possibly useful monographs via Google. This PDF includes some tables such as Table10.4 .

The following is a PowerPoint lecture which may also help



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