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Discuss coefficient of viscosity in the contex of stress and strain . |
Answer» Solution :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 ofviscosity 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. 
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