Relation Between Viscosity and Density

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Consider a fluid A and another fluid B. One is hair oil and another is milk, each of these is filled in one container. Now, let’s compare the two by pouring them into another container by switching on the timer.


Here, we would notice that the milk takes less time as compared to the hair oil, do you know why? It’s because the hair oil is more viscous or it is denser than the milk. So, why do we consider these terms as different when both of these carry the same meaning? 

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Difference Between Viscosity and Density

In the above example, we took two fluids viz: hair oil and milk. Now, let’s understand  how viscosity is related to density. 


Now, let’s take a look at another example. Consider fluid A as honey and another as water. At the microscopic level, honey has tightly bound particles, whereas water has particles that are far by some distance. So, when we differentiate in terms of distance each particle bears from another particle in a fluid, then it is density.


Now, let’s understand an example of a pickle. Let’s suppose that you have a big jar of pickle and want to transfer some pieces of it into the small jar, you would notice that the layers of oil come along with each piece and it takes a bit of time to reach another jar. You might have wondered why does this happen? Ummm, quite yes!


Well, it is because there is friction between the two layers and this friction hampers the fast flow of fluid, i.e., oil and the pickle pieces. So, the friction caused is called viscosity. 

Not only the liquid does, but air also has a viscosity that varies with temperature. I believe that through this example, you were able to understand what viscosity density is.


Relation Between Viscosity and Density

We don’t find the direct viscosity and density relation; however, both of these are affected by temperature.


As we can see that honey during winters have high density because it solidifies and in a solid-state, the interatomic particles are attached. When the same is kept under the sun or when the jar of honey is kept under the vessel containing hot water, the honey melts. So, what we notice is, the interatomic particles makes some distance under the effect of rising temperature and also the friction between the layers of honey while pouring it into another bowl reduces.

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The above scenario clearly explains the two following parameters:

  • Density and viscosity difference

  • Viscosity density relation

A subject like Physics not relies on theoretical knowledge only; it also focuses on mathematical equations, so let’s discuss the density viscosity equation:


Viscosity and Density Equation

According to the equation of kinematic viscosity, the equation says the following:

v = \[\frac{\mu}{\rho}\]

Here,

v = Kinematic viscosity.

A kinematic viscosity represents the dynamic viscosity of a fluid per unit density. The unit of the kinematic viscosity is m²/s. 

Dynamic viscosity = It is a force required to overcome the internal friction of any fluid. The unit employed for measuring the dynamic viscosity of a fluid is Pa.s (where ‘Pa’ stands for Pascal and ‘s’ stands for seconds).

μ = absolute viscosity. Absolute viscosity is a parameter for measuring the internal resistance in the fluid. 

=Density of the liquid or fluid or air. In MKS (Meter-kilogram-second), the unit of the density is kgm⁻³. In CGS or Centi-gram-second, the unit of the density is gcm⁻³.


Units of Kinematic Viscosity

The kinematic viscosity carries the three types of measuring units, let’s discuss these in a tabular form:


Type of unit

Unit

International standards or SI unit

kg/ms or Pascal.sec or N.s/m²

Centi-gram-second unit or CGS Unit  

Poise or gm/cm.sec

Foot-pound-second or FPS unit

Reyn or Pound.s/inchm²


Units of Absolute Viscosity

An absolute viscosity carries the three types of measuring units, let’s discuss these in a tabular form:  


Type of unit


International standards or SI unit

m² / s

Centi-gram-second unit or CGS Unit  

Stoke or cm² / s

Foot-pound-second or FPS unit

inch² / s


Dimensional Formula of Viscosity

We know that the formula for the viscosity is:

μ = \[\frac{F}{A}\] \[\frac{y}{U}\] 

⇒ \[\frac{FL}{L^{2}(L/T)}\] = \[\frac{FT}{L^{2}}\] ….(1)

We write this expression to write the fundamental unit of viscosity. So, rewriting the equation in the following way: 

As we know that the dimensional formula for the force, i.e., F is MLT⁻² , so putting this value in equation (1), we get:

⇒ \[\frac{MLT^{-2}T}{L^{2}}\]

After cancelling the common terms, we get the dimensional formula for the viscosity as:

μ = MLT⁻¹

FAQs (Frequently Asked Questions)

Question 1: Write the Value of the Viscosity and the Kinematic Viscosity of Air.

Answer: At the measuring temperature of 15 ⁰C, the value of viscosity of air is 1.81 x 10⁻⁵ kg/ms or 18.1 μPa. s or 1.81 x 10⁻⁵ Pa. s.

Similarly, at the measuring temperature of 15 ⁰C, the value of kinematic viscosity of air is 1.48 x 10⁻⁵ m²s or 14. 8cSt. 

Question 2: How Does Density Affect Viscosity?

Answer:  It is crystal clear from our context that both Viscosity and density are affected by temperature. It implies that for any given fluid, when the temperature is rising, the particle in it start moving apart, bringing down fluid density, and the value of viscosity decreases with lowering the viscosity.

Question 3: Why Does the Viscosity of Air Increase with Temperature?

Answer: When the temperature of gas increases, the kinetic energy of the molecules inside the gas also increases and the molecules start travelling at a higher speed. As a result, molecules start colliding with each other at a faster rate, and hence, the viscosity of air, i.e., increases with the temperature rise.

Question 4: State Density Versus Viscosity.

Answer: We define density as the measurement of the molecular weight of the molecules of gas/liquid/fluid. 

Density equals the number of molecules x molecular weight per volume occupied, while viscosity is a measurement of the intermolecular forces between the molecules in a gas/liquid/fluid.