The critical shear stress, at which the incipient motion of sediment takes place, is proportional to

where d is grain size.

Concept:

When the velocity through a channel is very low the bed sediment particles do not moves, but if the velocity increases gradually there will be a point of time when the bed sediment particles starts moving  with the flow.

This beginning of the movement of bed sediment particles is called as incipient motion of sediment.

• At incipient motion of sediment the shear stress applied by the flowing water on the bed sediment particles just exceeds the resistance of those particles and the particles start to move. This shear stress is called as critical shear stress.
• Incipient motion of sediment is also known as threshold point or critical condition.

The relationship between critical shear stress and diameter of the particle is best represented by Shield’s formula which is given by,

\({{\rm{F}}_{\rm{s}}} = \frac{{{{\rm{\tau }}_{\rm{c}}}}}{{{{\rm{\gamma }}_{\rm{w}}}{\rm{d}}\left( {{{\rm{S}}_{\rm{s}}} - 1} \right)}}\)

Where,

FS = Shield’s Entrainment function (a dimensionless number),

τc = Critical shear stress,

d = Diameter of the particles,

Ss = Specific gravity of the particles, and

γw = Specific weight of water

For a particular type of sediment material Fs is constant.