  We report a theory deriving bulk flow scaling for canonical wall-bounded
flows. The theory accounts for the symmetries of boundary geometry (flat plate
channel versus circular pipe) by a variational calculation for a large-scale
energy length, which characterizes its bulk flow scaling by a simple exponent,
i.e. $m=4$ for channel and 5 for pipe. The predicted mean velocity shows
excellent agreement with several dozen sets of quality empirical data for a
wide range of the Reynolds number (Re), with a universal bulk flow constant
$\kappa\approx0.45$. Predictions for dissipation and turbulent transport in the
bulk flow are also given, awaiting data verification.
