Discuss coefficient of viscosity in the contex of stress and strain .

Explanation

In figure laminar flow of liquid is shown.

A layer of liquid sandwiched between two parallel glass plates in which the lower plate is fixed and the upper one is moving to the right with velocity v
Liquid layers are shown between the glass plates .
Upper plate move with velocity v hence layer contact with it also move with velocity v.
On account of this motion , a portion of liquid, which at some instant has the shape of ABCD, take the shape of AEFD after short interval of time `Deltat`.
During time ,the liquid has undergone a shear strain of `(Deltax)/(l)` .The strain in a flowing fluid increases with time continuously.
In this case , the stress depend on the rate change of strain or stress depend on the rate change of strain or strain rate , that is `(Deltax)/(lDeltat) or (v)/(l)`
instead of strain itself. (Here `(Deltax)/(Deltat)` =velocityv)
Here shearing stress is `(F)/(A)` . Where A is the area of contact surface and F the viscous force F in the direction of tangent.
For fluid ,
coefficient of viscosity `=eta=("Shearing stress")/("Shear strain")`
`thereforeeta=((F//A))/((v//l))=(Fl)/(vA)` ....(1)
OR
`F=etaA((v)/(l))` ....(2)
The SI unit of viscosity is poiseiulle (Pl).
1 poiseiulle `1Nsm^(-2)=P_(a)*s`
CGS unit of coefficient of viscosity is poiseiulle
1 poiseiull =1 dyne S `cm^(-2)`
1 poiseiulle =10 pois
The dimensions of viscosity are `[M^(1)L^(-1)T^(-1)]` Generally thin liquids like water , alcohol are less viscous then thick liquids lke coal tar , blood, glycerine etc.
The viscosity of liquids decreases with temperature while it increases in the case of gases.