  Turbulence enhances the wall shear stress in boundary layers, significantly
increasing the drag on streamlined bodies. Other flow features such as
freestream pressure gradients and streamwise boundary layer growth also
strongly influence the skin friction. In this paper, an angular momentum
integral (AMI) equation is introduced to quantify these effects by representing
them as torques that alter the shape of the mean velocity profile. This
approach uniquely isolates the skin friction of a Blasius boundary layer in a
single term that depends only on the Reynolds number, so that other torques are
interpreted as augmentations relative to the laminar case having the same
Reynolds number. The AMI equation for external flows shares this key property
with the so-called FIK relation for internal flows [Fukagata et al. 2002, Phys.
Fluids, \textbf{14}, L73-L76]. Without a geometrically imposed boundary layer
thickness, the length scale in the Reynolds number for the AMI equation may be
chosen freely. After a brief demonstration using Falkner-Skan boundary layers,
the AMI equation is applied as a diagnostic tool on four transitional and
turbulent boundary layer DNS datasets. Regions of negative wall-normal velocity
are shown to play a key role in limiting the peak skin friction during the late
stages of transition, and the relative strengths of terms in the AMI equation
become independent of the transition mechanism a very short distance into the
fully-turbulent regime. The AMI equation establishes an intuitive, extensible
framework for interpreting the impact of turbulence and flow control strategies
on boundary layer skin friction.
