  Analytic predictions of mean velocity profile (MVP) and streamwise ($x$)
development of related integral quantities are presented for flows in channel
and turbulent boundary layer (TBL), based on a symmetry analysis of eddy length
and total stress. Specific predictions are the friction velocity $u_\tau$: ${
U_e/u_\tau }\approx 2.22\ln Re_x+2.86-3.83\ln(\ln Re_x)$; the boundary layer
thickness $\delta_e$: $x/\delta_e \approx 7.27\ln Re_x-5.18-12.52\ln(\ln
Re_x)$; the momentum thickness Reynolds number: $Re_x/Re_\theta=4.94[{(\ln
{{\mathop{\rm Re}\nolimits} _{\theta} } + 1.88)^2} + 1]$, all in good agreement
with empirical data.
