Viscosity

                                      -: Viscosity :-  

  •  Introduction :-

                         Viscosity is just one example of the engineering terms that applies to many other types of jobs, and is evident in everyday life. By definition, viscosity is-“quantity that describes a fluid's resistance to flow”, and explained in more detail “fluids resist the relative motion of immersed objects through them as well as to the motion of layers with differing velocities within them”. viscosity is a quantitative measure of a fluid’s resistance to flow.

                      When two layers of fluid, a distance 'dy' apart, move one over the other at different velocities, say u and u+du as shown in Fig. A viscosity together with relative velocity cause a shear stress acting between a fluid layers.
Top layer causes a shear stress on the adjacent lower layer while the lower layer causes a shear stress on the adjacent top layer. This shear stress is directly proportional to the rate of change of velocity with respect to y.

                                                                     τ ∝ du/dy

Where, μ is the constant of proportionality and is known as coefficient of dynamic viscosity, du/dy represents the rate of shear strain or velocity gradient.

  • Types of viscosity

1) Dynamic viscosity ;-It is also known as shear viscosity.Dynamic viscosity is measured by a fluid resistance to shearing flows, in which adjoining layers move parallel to one another, but at differing rates of speed.                                                                                               μ = τ du/dy                                                        
2) kinematic Viscosity :-It is the ratio of dynamic viscosity to the density.
It can be determined by dividing the absolute viscosuty by the fluid mass density.
                                           v =    μ/⍴
where, 
V = kinematic Viscosity  (m2/s) 
μ = absolute viscosity (N.s/m2)
⍴ = density (kg/m3)


Units :

In MKS and SI, the unit of kinematic viscosity is m2/sec, while in CGS units it is written as cm^2/sec. In CGS units of kinematic viscosity is also known as Stoke.     
Thus, one Stoke = 10^-4 m2/s. Centi-stoke means = 1/100 Stoke.

Newtons law of viscosity :-

  It states that shear stress on fluid element layer is directly proportional to the rate of shear strain. The constant of proportionality is called the co-efficient of viscosity. Mathematically it is expressed as,  
 τ ∝ du/dy  

  τ = μ du/dy
where, 
μ = Viscosity
τ =  Shear stress = F/A      
du/dy = rate of shear deformation.


  • Variation of Viscosity with temperature :-

•    Temperature affects the viscosity.
•    The viscosity of liquids decreases when the temperature increases, while the viscosity of gases increases with the increase of temperature.
•    This is due to reason that the viscous forces in a fluid are due to cohesive forces and molecular momentum transfer.
•    In liquids the cohesive forces are more important than the molecular momentum transfer, due to closely packed molecules and with the increase in temperature, the cohesive forces decrease with the result of decreasing viscosity.
 •    But in gases, molecular momentum transfer is more important than the cohesive forces. Molecular momentum transfer increases with the increase in temperature and hence viscosity of a gas increases.
•    For ordinary pressure, viscosity is independent of pressure and depends upon temperature only.

Problem :-

                                                 A fluid moves along length 0.75 m with velocity 2m/s and has shearing stress of 2 N/m

Given:
 Shear velocity du = 2 m/s, length dy = 0.75 m, shearing stress τ = 2 N/m2
  The shearing stress is given by,







  τ = μ du/dy
  2 =  μ 2/0.75
μ = 0.75 N.s/m2.

 Therefore, the dynamic viscosity is 0.75 N.s/m2.




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