Statement (I): The shear stress exerted by the stream flow on the
Statement (I): The shear stress exerted by the stream flow on the bed is responsible for the movement of bed sediment particles.
Statement (II): The sediment will move when the shear stress crosses a threshold limit designated as a critical shear stress τC
A. Both Statements (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
B. Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)
C. Statement (I) is true but Statement (II) is false
D. Statement (I) is false but Statement (II) is true (II) is true:
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Statement I: True
In sediment transport mechanism, incoherent soil (no cohesive forces between particles) like sand or gravel experience a drag force exerted by water in the direction of flow on the channel bed. This force is nothing but a pull of water and called shear force, tractive force or drag force. (Refer the following figure).
P1 & P2 = hydrostatic force, F = Friction on fed surface and A = Area of a given volume
Let us consider a channel of length L and cross-sectional area A.
The volume of water stored in this channel is AL.
Weight of water = γw AL
Component of the weight of water along the flow, H = γw AL Sin θ
Since θ is very small, we can say that,
θ ≈ Sin θ ≈ tan θ = S; where S is bed slope.
H = γw ALS
This horizontal force called Tractive force.
Average tractive force per unit wetted area called shear stress and it is given by
\({\rm{\tau }} = {\rm{\;}}\frac{{{{\rm{\gamma }}_{\rm{w}}}{\rm{ALS}}}}{{{\rm{Wetted\;perimeter\;}}\left( {\rm{P}} \right) \times {\rm{L}}}}\)
τ = γw RS (Where R is the hydraulic radius, R = A/P)
This shear stress is responsible for sediment transport.
Statement II: True
The critical shear stress is shear stress required to move a particle or grain of sediment of diameter ‘d’ in water on the bed. It is given by Shield’s expression:
τc = 0.056γwd(S - 1) (For channel bed)
Where S is the specific gravity of sediment material.
∴ If tractive effort is less than shear stress i.e. τ < τc then sediment will move on bed.
