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Viscosity and Newton's Law of Viscous Force

In case of steady flow of a fluid, when a layer of fluid slips or tends to slip on adjacent layers in contact, the two layers exert tangential force on each other which tries to destroy the relative motion between them. The property of a fluid due to which it opposes the relative motion between its different layers is called viscosity (or fluid friction or internal friction) and the force between the layers opposing the relative motion is called viscous force.
According to Newton’s hypothesis, the tangential force F acting on a plane parallel layer is proportional to the area of the plane A and the velocity gradient dv dx in a direction normal to the layer, as shown in Fig. 13, i.e.,
Fig. 13
F ∝ A and 51111.png
∴ 51105.png
or 51099.png
where η is a constant called the coefficient of viscosity. Negative sign is employed because viscous force acts in a direction opposite to the flow of liquid.
If A = 1, dv dx = 1, then η = F.
Hence, the coefficient of viscosity is defined as the viscous force acting per unit area between two layers moving with unit velocity gradient.
  • Units: dyne-s cm2 or Poise (CGS system); Newton-s/m2 or Poiseuille or decapoise (SI system).
    1 Poiseuille = 1 decapoise = 10 Poise
  • Dimension: [ML–1 T–1]
  • With increase in pressure, the viscosity of liquids (except water) increases while that of gases is practically independent of pressure. The viscosity of water decreases with increase in pressure.
  • From kinetic theory point of view, viscosity represents transport of momentum, while diffusion and conduction represent transport of mass and energy respectively.
  • The viscosity of thick liquids such as honey, glycerin, coaltar, etc, is more than that of thin liquids such as water.
  • The cause of viscosity in liquids is cohesive forces among molecules whereas in gases it is due to diffusion.
  • The viscosity of gases increases with increase of temperature, because on increasing temperature the rate of diffusion increases.
  • The viscosity of liquid decreases with increase of temperature because the cohesive force between the liquid molecules decreases with increase of temperature
    Relation between coefficient of viscosity and temperature (Andrade formula),
    where T = absolute temperature of liquid, ρ = density of liquid, and A and C are constants.

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