Assume a fluid flow which is rotational and viscous, passes over a flat plate with zero incidence. How will center of pressure move along the plate, if we increase upstream velocity. Does it move closer to the leading edge, or closer to the trailing edge?
I am not sure to understand your question...
Are you considering the standard Blasius problem? Is so, you know that dp/dy tends to vanish and the pressure dp/dx can be computed from the external (inviscid) solution deriving Bernoulli.
It is a simple question. There is a plate exposed to unidirectional uniform fluid flow with zero incidence. The plate would have its center of pressure calculated by the formula: Xcp=int(p(x).x.dx)/int(p(x).dx), where int is the integral, x the independent variable, dx the integrand variable, and p(x) is the pressure distribution on the point x, whilst x is measured from the front edge of the plate. I want to know, how Xcp would travel over plate surface (or simply along horizontal coordinate x), if we increse upstream velcity (U∞) at the leading eged (the front of the plate). No matter interpreting it through boundary layer or else, I am looking only for a qulitative sense of the movement of Xcp. Simply I want to know whether location of Xcp moves closer to the leading edge (the front of the plate) or to the trailing edge (the end of the plate), when we increase the value of free stream velocity.
Again, I think your question is not well posed...
1) the theory of the BL over a flat plate at zero AOA requires that the plate is semi-infinite, therefore your integral extends up to x->+Inf
2) the pressure distribution is based on the external flow velocity (dp/dy->0) according to Bernoulli. Therefore, on a flat plate if the Uinf velocity is uniform dp/dx=0 and p is uniform along the plate.
This is the deficiency and impracticality of BL to which I do not have a trust. How boundary layer claims to be a theory, but cannot predict such an important formula (for center of pressure)!!!.
So what does happen when the plate is of finite length? Is the integral calculable or at least qualitatively interpreted? Have you gotten any further auxiliary insight over the Xcp variation?
A finite lenght plate will change the outflow condition and the BL theory is not valid. The Blasius theory has nothing to do with the evaluation of the pressure center.
As a rude approximation, you could think to an ellipse at zero AOA having the thickness going to zero. For viscous flow the parameter that has relevance is the Reynolds number and it increases for increasing inflow velocity. The flow becomes transitional and then turbulent. Separation and vortical structures will appear
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