  The Karman constant \kappa - widely used in atmospheric science and
engineering turbulence modelling, and proposed by Prandtl in 1925 and von
Karman in 1930 to describe the mean velocity of a turbulent wall-bounded flow -
leads to a logarithmic profile in an overlap region near the wall. For over
eighty years, its value was believed to be ~0.41. But more recently, many argue
that it is not a constant, because of measured variations in different flows
and at different Reynolds numbers (Re). Here, a multi-layer analytic theory is
shown to lead to a re-interpretation of \kappa as a global constant for both
the overlap region and outer flow, and to yield a new method for its
measurement. The newly determined value is 0.45 for both channel and pipe. It
is shown that this new \kappa, together with other wall constants, yields a 99%
accuracy in the prediction of mean velocity data at all points in high Re (up
to 40 million) pipe flow. The theory also describes finite Re effect, and
discovers a transition at the friction Re (i.e. Re_\tau)=5000. An accurate
model for the prediction of turbulent transport in canonical pipe and channel
flows is achieved here, and we propose the model to be valid for a wide class
of turbulent flows.
