Figure 2.8. Hydraulically rough boundary.
Figure 2.9. Velocities in turbulent flow.
The two components of velocity in Figure 2.9a can be written as:
v x = v x + v′x
v y = v y + v ′y
where v x and v y are the time-averaged mean velocities in the x and y direction and vx′ and vy′
are the fluctuating components.
Through theoretical investigation it has been found that turbulence generates shear stress given
τ = - ρv ′x v ′y