  The direct measurement of wall shear stress in turbulent boundary layers
(TBL) is challenging, therefore requiring it to be indirectly determined from
mean profile measurements. Most popular methods assume the mean streamwise
velocity to satisfy either a logarithmic law in the inner layer or a composite
velocity profile with many tuned constants for the entire TBL, both of which
require reliable data from the inner layer. The presence of roughness and
pressure gradient brings additional complications where most existing methods
either fail or require significant modification. A novel method is proposed to
determine the wall shear stress in zero pressure gradient TBL from measured
mean profiles, without requiring near-wall data. The method is based on the
stress model of Kumar and Mahesh [Phys. Rev. Fluids 6, 024603 (2021)], who
developed accurate models for mean stress and wall-normal velocity in zero
pressure gradient TBL. The proposed method requires a single point measurement
of mean streamwise velocity and mean shear stress in the outer layer,
preferably between $20$ to $50 \%$ of the TBL, and an estimate of boundary
layer thickness and shape factor. The method can handle wall roughness without
modification and is shown to predict friction velocities to within $3 \%$ over
a range of Reynolds number for both smooth and rough wall zero pressure
gradient TBL. In order to include the pressure gradients effects, the work of
Kumar and Mahesh [Phys. Rev. Fluids 6, 024603 (2021)] is revisited to derive a
novel model for both mean stress and wall-normal velocity in pressure gradient
TBL, which is then used to formulate a method to obtain the wall shear stress
from the profile data. Overall, the proposed method is shown to be robust and
accurate for a variety of pressure gradient TBL.
