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# Viscosity | QnA | Properties of Fluid | Fluid Mechanics | By Ashutosh Nautiyal

What is Viscosity?Viscosity is the property of fluid by virtue of which it offers resistance to the movement of one layer of fluid over an adjacent la

## Viscosity Viscosity

## Describe Viscosity.

• Viscosity is the property of fluid by virtue of which it offers resistance to the movement of one layer of fluid over an adjacent layer.

## Derive the formula for Viscosity. Velocity Variation near a Solid Boundary

• Let us consider two layers of fluid, at a distance dy apart, moving one over the other at different velocities.

• The viscosity together with relative velocity causes shear stress between fluid layers.

• The upper layer causes shear stress on the adjacent lower layer, while the lower layer causes shear stress on the adjacent upper layer.

• This shear stress is proportional to the rate of change of velocity with respect to y.

• Mathematically,  τ ∝ du/dy

•  τ = μ (du/dy)

• where μ is the constant of proportionality and is called the coefficient of viscosity or dynamic viscosity

• du/dy represents the rate of shear strain or rate of shear deformation or velocity gradient

• Now, μ = τ /(du/dy)

• Thus, the viscosity may also be defined as shear stress required to produce a unit rate of shear strain.

## Name a few units of Viscosity.

• Since, μ = τ /(du/dy)

N.(m^(-2))
•  μ = ____________

m(s ^(-1))/m

•  μ = N.s/m2 = Pa.s

• The SI unit of viscosity is N.s/m2.

• Its MKS unit is kgf-sec/m2.

• Its CGS unit is dyne-sec/cm2.

•  For practical purposes, another unit poise is used after the name of a scientist, Poiseuille.

• 1 N/m2 = 10 poise = 1000 centipoise

## Describe Kinematic Viscosity.

• The rate of dynamic viscosity(μ) to the mass density(ρ) of a fluid is called kinematic viscosity.

• Generally, it is denoted by ν.

• ν = μ/ρ

• The SI unit of kinematic viscosity is m2/s.

• Its CGS unit is cm2/s.

• Another unit of kinematic viscosity is stoke.

• 1 m2/s = 10000 stokes

## Describe Newton's Law of Viscosity.

• Newton's Law of Viscosity states that the shear stress(τ) on a fluid element is directly proportional to the rate of shear strain.

• τ∝du/dy

• τ = μ(du/dy)

• where μ is called the coefficient of viscosity

• The fluids which obey this law are known as Newtonian fluids.

• The fluids which don't obey this law are known as Non-Newtonian fluids.

## Describe Variation of Viscosity with Temperature.

• Temperature affects viscosity.

• For liquids, viscosity decreases with the increase of temperature because, in liquids, the cohesive forces predominate the molecular momentum transfer(due to closely packed molecules) and when the temperature increases, viscosity decreases(due to decrease in cohesive forces).

• For gases, viscosity increases with the increase of temperature because, in liquids, the molecular momentum transfer predominates the cohesive forces(due to less closely packed molecules) and when the temperature increases, viscosity increases(due to increase in molecular momentum transfer).

*Self Typed
*Source- Books, Internet, Self-Analysis

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