Vertical pressure profile in the boundary layer?

Within the framework of my research, I make the assumption that the vertical logarithmic profile of wind velocity in the boundary layer induces a vertical pressure profile. This result is confirmed experimentally since when I measure the difference in pressure between 2 points located at 15 and 45 cm of the ground (ddp).





Moreover, my experimental relation between ddp and horizontal wind velocity is closed to that which one would obtain by considering that it rises, by Bernoulli, of the vertical gradient of the horizontal wind component.





However, Bernoulli is not applicable since I m not on a current line and I m in turbulent conditions.





How can I justify the presence of this gradient?








thank you for your help

Vertical pressure profile in the boundary layer?
No, Bernouilli is not applicable here.


I think you need to apply the complete Navier-Stokes equations for turbulent, compressibile flow amplifying what is happening in the boudary layer and with some simplifications to the equation (like gravity, I think). Of course the boundary conditions on the boudary layer must coincide with the boundary conditions in the external flow. If I remember, when the equation is solved, you get a velocity profile depending from the distance from the beginning of the boundary layer (i.e. vertical) expressed as the ratio of the velocity to the "unperturbed" velocity (the one in the external flow). Once you have the velocity obtaining the pressure profile is not to difficult. Hope I've given you some advice.
Reply:♣ marie, I see the goal of your experiment;


but still can’t understand what is ddp short for; how is that "experimental relation is closed" !? And why don’t you just avoid turbulence? Can you express it more clearly?





♠ ah-ah, ? does it mean: 1) you’ve got abundant reliable experimental data, 2) you tried a couple of formal math models that contain some undefined parameters;


♣ So the task is to find now the most satisfactory model with the less number of parameters the better, isn’t it? if so use regression analysis!


♦ I’m not much particular in fluid dynamics, yet I guess here are many who could help you with maths; unless I sound a full dumb-a.s.s and you find my suggestions of some use click me through my profile for further discussion!