Tractive force theory

TRACTIVE FORCE THEORY

  • In the study of mechanics of sediment transport, the soil particles are always considered as incoherent.
  • Most of the river beds are made up of sand and gravel and as such assumption in regard to soil being incoherent is correct.
  • The basic mechanism that controls the sediment transport, is the drag force exerted by water in the direction of flow on the channel bed.
  • This drag force is also known as tractive force or shear force.
  • This force is nothing but a pull of water on the wetted area of the channel.
  • Consider a channel of length L and cross-sectional area A.
  • The volume of water in this length of channel would be A × L.
  • If w is the unit weight of water, then weight of water stored in this length (L) of the channel will be wAL. Weight of water acting in vertical direction = wAL.
  • The horizontal component of this weight = wAL sin θ.
  • But θ is slope of the channel which is represented by S. Horizontal component of weight = wALS.
Fig. 18.3. Flow of water in channel and forces acting on silt at bed.
Flow of water in channel and forces acting on silt at bed.
  • This horizontal force exerted by water is nothing but tractive force.
  • If average tractive force per unit of wetted area is τ, then
  • Hence average unit tractive force also know shear stress is given by τ = wSR.

where

w = Unit of weight of water

S = Longitudinal slope of the channel

R = Hydraulic mean depth H.M.D.

  • In the case of wide open channels, the value of hydraulic mean depth (H.M.D.) is almost equal to depth of the channel.
  • Hence tractive force can be written as follows also

τ = wSD

  • If tractive force becomes greater than the frictional resistance between particles, the particles are set in motion.
  • The resistance of sediment to motion in proportional to the diameter d of the particle and the submerged weight of sediment in water.
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