  We prove an estimate of total (viscous plus modelled turbulent) energy
dissipation in general eddy viscosity models for shear flows. For general eddy
viscosity models, we show that the ratio of the near wall average viscosity to
the effective global viscosity is the key parameter. This result is then
applied to the 1-equation, URANS model of turbulence for which this ratio
depends on the specification of the turbulence length scale. The model, which
was derived by Prandtl in 1945, is a component of a 2-equation model derived by
Kolmogorov in 1942 and is the core of many unsteady, Reynolds averaged models
for prediction of turbulent flows. Away from walls, interpreting an early
suggestion of Prandtl, we set \begin{equation*} l=\sqrt{2}k^{+1/2}\tau,
\hspace{50mm} \end{equation*} where $\tau =$ selected time scale. In the near
wall region analysis suggests replacing the traditional $l=0.41d$ ($d=$ wall
normal distance) with $l=0.41d\sqrt{d/L}$ giving, e.g., \begin{equation*}
l=\min \left\{ \sqrt{2}k{}^{+1/2}\tau ,\text{ }0.41d\sqrt{\frac{d}{L}} \right\}
. \hspace{50mm} \end{equation*} This $l(\cdot )$ results in a simpler model
with correct near wall asymptotics. Its energy dissipation rate scales no
larger than the physically correct $O(U^{3}/L)$, balancing energy input with
energy dissipation.
