I would like to find this integral analytically by using “Cauchy Residue Theorem”, but my problem is what contour is suitable?
\int {\frac {\exp(-M\omega) \exp(iN\omega)} {\omega^5(\frac{\omega^4}{f^4} + \frac{(\omega^2)(4\zeta^2-2)}{f^2}+ 1)}d\omega
From 0 to \infty
Where, M, N,f and...
I am really confused. Would you please tell me what the turbulent boundary layer thickness is on a flat plate?
There is a well-known Schlichting formula in the previous editions of his book “boundary layer theory”, which is:
\delta = 0.37 X Re^{-0.2}
But actually I could not find this...
Numerical Integration
I could not obtain the numerical answer for following integrals, actually they tend to infinity.
\int {\frac {(e^{-M\omega}) \cos(N\omega)} {\omega^5(\frac{\omega^4}{f^4} + \frac{(\omega^2)(4\zeta^2-2)}{f^2}+ 1)}d\omega
\int {\frac {(e^{-M\omega}) \sin(N\omega)}...
Residue of poles of 5th order at 0
The integrand has poles of 5th order at 0, to find residue may be we should
\lim {\frac{d^4}{d\omega^4}\frac {\omega^5 e^{-M\omega} e^{iN\omega}} {\omega^5(\frac{\omega^4}{f^4} + \frac{(\omega^2)(4\zeta^2-2)}{f^2}+ 1)}
\omega\rightarrow 0
and in...
Residue
We assume that M, N, fand \zeta are real and positive and \zeta\ll 1.
Actually I solved the integral but I found some discrepancies.
I would like to find the residue at following pole.
-f\sqrt{(1-2 \zeta^2) - i2\zeta \sqrt{ (1-\zeta^2)}}
As I mentioned \zeta\ll 1 so I...
You responded that it is possible to have a “fully developed turbulent flow over a single plate” and the only variable here is the Reynolds' number.
I am interested in FULLY DEVELOPED, which means its velocity profile does not depend on the streamwise coordinate.
I would like to know if it...
I would like to find the attached integral analytically by using “Cauchy Residue Theorem”.
I am wondering if there is any numerical solution for this integral.
Thanks
\int {\frac {\exp(-M\omega) \exp(iN\omega)} {\omega^5(\frac{\omega^4}{f^4} + \frac{(\omega^2)(4\zeta^2-2)}{f^2}+...
Random vibration and FEM
I am wondering if deterministic method such as FEM is reliable for computation of random response to dynamic system.
We are developing a method to predict the response of a flat shell element to a pressure filed arising from the fully developed turbulent boundary...
fully developed turbulent flow over plate
Is it possible to have a “fully developed turbulent flow” over plate?
I am interested is incompressible subsonic flow and I know that the fully developed turbulent flow, i.e., constant velocity profile can happen inside pipes or channels or between...
fully developed turbulent flow over plate
Is it possible to have a “fully developed turbulent flow” over plate?
I am interested is incompressible subsonic flow and I know that the fully developed turbulent flow, i.e., constant velocity profile can happen inside pipes or channels or between...