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

(2.67)

and

v y = v y + v ′y

(2.68)

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

by

τ = - ρv ′x v ′y

(2.69)

2.17

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