Open Channel Flow - Sediment Transport in Irrigation Canals: A New Approach - page 13

layers is proportional to the velocity gradient, ∂u / ∂y , in the direction
perpendicular to the layers.

µ ∂u
∂y

τ = (2.1)

The constant µ is the dynamic viscosity. Fluids, such as water, that
satisfy Newton's criterion are known as Newtonian fluids and show lin-
earity between shear stress and velocity gradient. When the viscous forces
are related to inertial forces, the ratio is characterized by the kinematic
viscosity ν .

µ
ρ

ν = (2.2)

The unit of dynamic viscosity is Pa s (Pascal second) and is identical to

1 N/s m 2 . The unit of kinematic viscosity is m 2 /s. The viscosity of water
decreases with an increase in temperature, see Table 2.1.

·

Table 2.1. Kinematic viscosity of water as a function of the temperature T .

T ( ◦ C)

0 5 10 14 20 25 30

ν (10 − 6 m 2 /s)

1.79 1.52 1.31 1.14 1.01 0.90 0.80

Viscosity is the main factor resisting motion in laminar flow. However,
when the velocity has increased to the point at which the flow becomes
turbulent, pressure differences resulting from eddy currents rather than
viscosity provide the major resistance to motion.
Significant dimensionless numbers in open channels are the Froude
number and the Reynolds number. The Froude number gives the ratio
between the inertial force and the force due to the gravity and is
represented by:

ρL 2 v 2
ρgL 3

v 2
gL

Fr 2

= = (2.3)

where:
v

= mean velocity (m/s)

g = acceleration due to gravity (m/s 2 )

L = a characteristic length, e.g. water depth (m)

density (kg/m 3 ) ρ =

kinematic viscosity (m 2 /s) ν =

The Froude number differentiates between sub- and supercritical flow.
When the Froude number is one, the flow is critical. For numbers larger
than one the flow is supercritical.