# Dynamic and kinematic viscosity and how they relate

• mitch_1211
In summary, the overall viscosity of a liquid or gas is related to both kinematic and dynamic viscosities. The kinematic viscosity of air is approximately 1.4e-5, while that of water is approximately 1e-6. However, the dynamic viscosity of water is greater than that of air. This means that water is more viscous than air. Dynamic viscosity is typically the more commonly used and physically meaningful quantity when describing the overall viscosity of a fluid.
mitch_1211
I have been looking into how the overall viscosity of a liquid/gas is related to kinematic and dynamic viscosities.

I have used nwater = 1e-3 Pa.s
nair = 17.4e-6 Pa.s
densitywater = 1000 kgm^-3
densityair = 1.3 kgm^3

and kinematic viscosity v = n/density

So vair ~ 1.4e-5
vwater ~ 1e-6

So here the dynamic viscosity of water is greater than that of air, but the kinematic viscosity for water is less that that of air.

Does this mean that air is the more viscous fluid? How would one use there two properties to describe the overall viscosity of a fluid?

Mitch

Typically, when people refer to viscosity, they are referring to the dynamic viscosity, not the kinematic viscosity. So, I would describe water as more viscous than air.

cjl said:
Typically, when people refer to viscosity, they are referring to the dynamic viscosity, not the kinematic viscosity. So, I would describe water as more viscous than air.

To add onto this, viscosity's chief use, relating velocity gradients in a fluid to shear stresses, involves dynamic viscosity, $\mu$. Kinematic viscosity is more of a value of convenience used because it can help simplify the notation sometimes. Dynamic viscosity is the more physically meaningful quantity in the most basic sense.

I was thinking that was the case. Thank you both for the explanations.

ell, thank you for bringing up this topic. I can provide some insights into the relationship between dynamic and kinematic viscosity and how they contribute to the overall viscosity of a fluid.

First, let's define dynamic and kinematic viscosity. Dynamic viscosity is a measure of a fluid's resistance to flow under an applied force or stress. It is typically represented by the symbol "n" and has units of Pa.s (Pascal seconds). On the other hand, kinematic viscosity is a measure of a fluid's resistance to flow due to its internal friction and is represented by the symbol "v". It has units of m^2/s (square meters per second).

The relationship between these two viscosities can be described by the equation v = n/p, where "p" is the density of the fluid. As you have correctly calculated, the kinematic viscosity of water is lower than that of air, despite water having a higher dynamic viscosity. This is because water is denser than air, resulting in a lower kinematic viscosity.

To answer your question, the overall viscosity of a fluid cannot be determined solely by its dynamic or kinematic viscosity. Both properties play a role in determining the fluid's resistance to flow. In fact, the overall viscosity of a fluid is a combination of these two viscosities, along with other factors such as temperature and pressure.

In summary, dynamic and kinematic viscosity are important properties that help us understand the behavior of fluids. While they may seem contradictory at first, they both contribute to the overall viscosity of a fluid and cannot be used interchangeably. Further research and experimentation are necessary to fully understand the complexities of fluid viscosity.

## 1. What is the difference between dynamic and kinematic viscosity?

Dynamic viscosity, also known as absolute viscosity, is a measure of a fluid's resistance to flow under an applied force. It is typically represented by the symbol "μ" and measured in units of Pascal-seconds (Pa·s) or centipoise (cP). Kinematic viscosity, on the other hand, is a measure of a fluid's resistance to flow due to its internal friction and is expressed as the ratio of dynamic viscosity to density. It is typically represented by the symbol "ν" and measured in units of square meters per second (m2/s) or centistokes (cSt).

## 2. How are dynamic and kinematic viscosity related?

The relationship between dynamic and kinematic viscosity is given by the formula ν = μ/ρ, where ν is kinematic viscosity, μ is dynamic viscosity, and ρ is density. This means that the kinematic viscosity of a fluid is directly proportional to its dynamic viscosity and inversely proportional to its density.

## 3. How is dynamic viscosity measured?

Dynamic viscosity can be measured using various methods, such as a viscometer or a rheometer. These instruments apply a known force to a sample of fluid and measure the resulting flow rate. The higher the force required to achieve a certain flow rate, the higher the dynamic viscosity of the fluid.

## 4. What factors affect the dynamic and kinematic viscosity of a fluid?

The dynamic and kinematic viscosity of a fluid can be affected by several factors, including temperature, pressure, and the composition and structure of the fluid. Generally, as temperature increases, the viscosity of a fluid decreases, while as pressure increases, the viscosity of a fluid increases. The molecular structure and composition of the fluid can also impact its viscosity, with more complex molecules and higher concentrations of dissolved substances typically resulting in higher viscosities.

## 5. How is viscosity important in various industries?

Viscosity plays a crucial role in many industries, including food and beverage, pharmaceuticals, petroleum, and automotive. In the food and beverage industry, viscosity is important for ensuring the desired texture and consistency of products such as sauces, dressings, and beverages. In the pharmaceutical industry, viscosity is critical for the proper dosing and administration of medications. In the petroleum industry, viscosity is used to determine the quality and flow characteristics of crude oil. In the automotive industry, viscosity is important for the lubrication of engine components to reduce friction and wear.

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