1. Turbulent Flow
The Reynold’s experiment demonstrates how the mechanism of fluid flow can
change as flowrates (or, more precisely, the Reynolds number) increase. The flow
structure shifts from being laminar to turbulent. With turbulence, there is a random
fluctuating component to the velocities and pressure.
vx(x,y,z,t)
vx(x,y,z) t t t =
v'x(x,y,z,t)
Time averaged velocity
with net displacement
Fluctuating component
with no net displacement
vx = vx(x,y,z) v'x(x,y,z,t)
vx is the time averaged component of the turbulent velocity vx.

2. xy = - dvx -  v'xv'y Turbulent Flow v'x = 1  v'x(x,y,z,t) dt = 0
t1 o
vx = 1  vx(x,y,z,t) dt
t1 o
Length of t1 is much greater than
duration of a flucuation y
vx = vx(y)
vy = v'y and vy = v'y = 0
Overall motion is only in the x-direction for this
flow field. x
In laminar flow, we said frictional force imparted momentum from one
layer to another. Fluid did not cross from one lamina to another. In
turbulent flow, fluid elements can cross from one layer to the next due
to the fluctuating velocity in the y-direction. These impart momentum
in the x-direction.
Reynolds Stresses
xy = - dvx -  v'xv'y dy