# Turbulent Boundary Layer Thickness as Velocity Increases

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
plot(U,lam_lay,U,lam_lay2,U,turb_lay)
xlabel('Velocity (m/s)')
ylabel('Boundary Layer Height (m)')
legend('Laminar Boundary', 'Turbulent Boundary')

• 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 $1/U^{1/5}$.
– TRF
Jan 5 '17 at 19:11
• 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. Jan 5 '17 at 23:03

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