Viscosity in Fluid Mechanics

Viscosity is friction of fluids and it also describes internal resistance of flow of fluid. In this article, we are going to discuss what dynamic viscosity and kinematic viscosity are, their definitions, applications of dynamic and kinematic viscosity and finally differences between kinematic viscosity and dynamic viscosity.

What is Viscosity?

Viscosity can be defined as resistance of fluid to flow. It is an important property of fluid and sign of internal friction. This resistance is caused from forces of attraction between fluid molecules. In simple term, viscosity is internal friction of fluid and also referred as thickness of fluid.

Viscosity is property of fluid that finds out amount of resistance of fluid to shear stress. Viscosity is property of fluid its offers resistance to movement of one layer of fluid above next layer. In simple words it is defined as property which offers resistance to flow. Check Brake System Types, Functions, and Types of Brakes in automobile

What is Viscosity in Fluid Mechanics?

Fluid has high viscosity of high internal resistance to flow. One way to think about viscosity is that it is amount of force need to get that substance moving. It is force per unit area, so viscosity is equal to force divided by area. Also, it is directly proportional to what is called shear rate. This shear rate is speed that liquid is moving divided by distance that it moves. Shearing forms whenever fluid moved physically like pouring, spraying, spreading, mixing etc.

They move slower than fluid having low viscosity. So some fluids move faster than other. Viscosity states that, shear stress between adjacent fluid layers is relative to velocity between two layers. But shear stress ratio to shear rate is constant, for given temperature and pressure. Such a flow where velocity u in x direction changes in Y direction is called shear flow.

Examples of Viscosity

For example, take two bottles, let’s have honey in one bottle and other have water. If you make small hole at bottom of bottle, so which bottle gets emptied first. Here we are talking about is viscosity. Therefore, high viscous fluids need more force to move than less viscous materials. In above example, water has lower viscosity than honey.

Hence, water gets emptied than honey. So viscosity of fluid varies with temperature and pressure. Read Newton’s Law of Viscosity and Equation. This fluid will only flow if enough energy is applied to overcome these forces. If you need to move through fluid, fluid has to flow across it or around it. Hence, energy needed for moving body through fluid is directly related to fluid resists flow.

Types of Viscosity of fluid

There are two ways to measure fluid’s viscosity. It can either be expressed as dynamic viscosity or kinematic viscosity. In reality, they are two much different terms. This relationship between these two properties is quite simple.

Dynamic Viscosity

Dynamic Viscosity is also known as absolute viscosity. It also measure fluid resistance to shear flow, when external force is applied. It is useful for telling behavior of fluids under stress. Mainly, it is useful in telling non-Newtonian fluids by how viscosity changes as shear velocity changes. As a result, these two material properties may not always be so easy.

In other words, dynamic viscosity is defined as tangential force per unit area need to move fluid in one horizontal plane with other plane while fluid molecules will maintain unit distance. Dynamic viscosity is directly proportional to the shear stress and is expressed by symbol (µ) and has the SI units of N s/m2 (Newton second per square meter).

What is kinematic viscosity?

Kinematic viscosity is ratio of dynamic viscosity to fluid of density. It is measure of fluid’s resistance to shear flow under gravity weight. Here force is applied weight and measure of fluid resistance to flow, when no external forces except gravity is acting. But it is more useful in telling Newtonian fluids.

In some cases, inertial force of fluid is also need with viscosity measurement. On other hand, inertial force of fluid depends on density of fluid. Kinematic viscosity is dividing absolute viscosity of fluid with fluid density.  Thus, kinematic viscosity is termed as V and it has units of meters squared divided by seconds.


Where v is kinematic viscosity, µ is dynamic viscosity and ρ is density.

Coefficient of Dynamic Viscosity

Coefficient of dynamic viscosity (π) is defined as shear force per unit area need to pull one fluid layer with unit velocity passes another layer unit from distance away from fluid.

T = \pi \frac{d_{x}}{d_{y}}=\frac{Force}{Area}/\frac{Velocity}{Distance}=\frac{Force \times Time}{Area} \quad or \quad \frac{Mass}{Length \times Time}

Units of Viscosity

As per Newton seconds per square meter is N\quad s\quad m^{-2}  or kilograms per meter per second is  kg\quad m^{-1} \quad s^{-1}. But note that coefficient of viscosity is measured in poise (P), 10 P = 1  kg\quad m^{-1} \quad s^{-1}.

Viscosity of Dimensions is M\quad L^{-1}T^{-1}  and values for water are 1.14 \times 10^{-3}kg \quad m^{-1}s^{-1} or for air is 1.78 \times 10^{-5}kgm^{-1}s^{-1}

Formula for Viscosity

According to  Newton’s law of viscosity, taking direction of motion as ‘x’ direction and as velocity of fluid in ‘x’ direction at distance ‘y’ from boundary, shear stress () in ‘x’ direction is given by formula. In this equation, sheer rate is known as du/dy. This refers to velocity divided by distance. Kinematic viscosity is ratio of dynamic viscosity and density of fluid.

\mu=\pi \quad \frac{dv_{x}}{dy}   Where µ – Viscosity, T-Shear Stress and Du/ Dy – Rate of shear deformation

Difference between Kinematic Viscosity and Dynamic Viscosity

Dynamic and Kinematic viscosity are two important concepts in fluid mechanism. These two concepts have many applications in fields like fluid dynamics, fluid mechanics and even medical science. So you need to understand concepts of dynamic viscosity and kinematic viscosity are need in above fields.

  • Dynamic viscosity also called absolute viscosity and kinematic viscosity is called diffusivity of momentum.
  • Dynamic viscosity is independent of the density of the fluid, but kinematic viscosity depends on the density of the liquid.
  • Kinematic viscosity is equal to the dynamic viscosity divided by the density of the liquid.
  • Dynamic viscosity is symbolized by either ‘µ’, while Kinematic viscosity is symbolized by ‘v’.
  • Dynamic viscosity is quantitative expression of fluid’s resistance to flow, while Kinematic viscosity is the ratio of fluid’s viscous force to inertial force.

Method of Viscosity

There are two factors of viscosity of fluid. Following are various methods used to measure viscosity of fluid. To know more details about see Magneto Ignition System, Parts, Working, Advantages & Disadvantages

Cohesion of intermolecular force

Any layer in moving fluid tries to drag next layer to move with equal speed due to strong forces between molecules and thus effect of viscosity. Since, cohesion decreases with temperature and liquid viscosity is also same.

Molecular exchange

As viscosity increases, molecular motion of fluid particles increases with temperature increases accordingly. Therefore, except for special cases viscosity of both gases and liquids will increase temperature.

Difference of Viscosity

Viscosity of fluid varies with both temperature and pressure and depends on state of fluid such as liquid and gases.

Viscosity of liquids

For liquids, viscosity increases with increasing pressure because amount of free volume in internal structure decreases due to compression. As a result, molecules move less freely and internal friction forces increase.  Since, Viscosity of liquids is incompressible unless pressure increase is important but viscosity does not change much. Below equation follows-

\mu=Ae^{B/T} where T is absolute temperature and A & B are constants

Gases of viscosity

Viscosity of an ideal gas is independent of pressure and this is almost true for gases. In gases, viscosity arises because of transfer and exchange of molecular momentum. So double pressure gives you double number of molecules arriving at surface, but on average they will come from half as far away and cancel out it effects.

Importance of fluid viscosity in various applications

  • Viscosity is measured during variety of lubricants for machines. For example, high thick oils are chosen for slowly moving parts while low thick lubricants used for fast moving parts.
  • Viscosity data help to forecast how fluid act in particular condition that helps in machine designs.
  • Viscosity holds liquid anywhere they placed. If fluid has no viscosity they can flow forever without any internal resistance and they can flow out of container.
  • For some application, viscosity must be just in time to get desirable properties. For example, if viscosity of paint is very low, it will run down walls. In simple way, if viscosity is high, then it is tough to apply paint on wall.
  • So heat depends on viscosity.