[Physics Class Notes] on Relation Between Viscosity and Density Pdf for Exam

Consider 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? 

 

 

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 apart. So, when we differentiate in terms of the 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 pickles 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 this happened? 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.

 

The key differences between viscosity and density are given in the following table.

 

Measuring Dynamic Viscosity

A rotational viscometer is one of the more popular types of instruments, and it is used to measure dynamic viscosity. In a liquid sample, this instrument rotates a probe. Viscosity is evaluated by measuring the force or torque needed to rotate the probe.

 

The rotational viscometer is especially useful in measuring non-Newtonian liquids. When non-Newtonian liquids are exposed to different conditions, they change viscosity. For instance, some non-Newtonian liquids increase in viscosity with an increase in applied force, whereas other non-Newtonian liquids show a decrease in viscosity with an increase in applied force.

 

As the probe moves in the liquid, the rotational viscometer adjusts its turning speed. The viscometer determines the variation in the viscosity of the sample as the speed, sometimes referred to as shear rate. The unit of measure for the dynamic viscosity is denoted as Centipoise (cP).

 

Measuring Kinematic Viscosity

There are few methods to find the kinematic viscosity of a fluid. The most common method to measure the kinetic viscosity is by determining the time it takes a fluid to flow through a capillary tube. The time is converted directly to kinematic viscosity with the help of a calibration constant provided for the specific tube. The unit of measure of kinematic viscosity is Centistokes (cSt).

 

A primary difference between the dynamic and kinematic viscosity measurements is density. With density, the conversion between a kinematic and a dynamic viscosity can be carried out. The formula for the conversion from kinematic to dynamic and from dynamic to kinematic is:

 

 

For a given sample, dynamic viscosity will always be the higher number with a density greater than one.

 

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, honey during winters has 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 make some distance under the effect of rising temperature and also the friction between the layers of honey while pouring it into another bowl reduces.

 

 

The above scenario clearly explains the two following parameters:

 

Viscosity and Density Equation

A subject like Physics does not rely on theoretical knowledge only; it also focuses on mathematical equations, so let’s discuss the density viscosity equation. According to the equation of kinematic viscosity, the equation says the following:

 

[v = frac{mu}{p}]

 

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:

 

Units of Absolute Viscosity

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

 

Dimensional Formula of Viscosity

We know that the formula for the viscosity is:

 

[mu = frac{F}{A}frac{y}{U}]

[= frac{FL}{Lsurd(frac{L}{T})}]

= [frac{FT}{L^{2}}]

 

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

 

μ = MLT⁻¹

 

Dimension of coefficient of viscosity

The coefficient of viscosity is η

 

Dimension of viscous force is [ M L T -2]

 

Dimension of length is [ L ]

 

Dimension of velocity is [ L T -1] 

 

Dimension of the area is L2

 

η = [ M L T -2 L L T -1 L2]

 

η = [ M L-1 T -1 ]

 

What is the density and viscosity of water?

Pure water has its highest density at 4.0°C = 1000 kg/m3.

 

Water – Density Viscosity Specific Weight.

 

How is viscosity determined?

Viscosity is defined as the measure of the resistance of a substance to a motion under an applied force. The viscosity is generally expressed in centipoise (cP), which is the equivalent of 1 mPa s (millipascal second). Shear stress is the force per unit area required to move one layer of fluid in relation to another.

 

How is density determined?

Density is a mass of a unit volume of a material substance. The formula for calculating density is,

 

[d = frac{M}{V}],

 

Where d = density, 

M = mass, 

V = volume.

 

Conclusion

Newtonian liquids have an inherent viscosity that does not change with the change in the force applied to the liquid. This inherent viscosity can be accurately determined with a capillary-type apparatus, using gravity to move the fluid. Alternatively, non-Newtonian fluids exhibit wide variations in viscosity based on the applied force. These require testing with rotational viscometers in order to measure changes over time and over a range of applied forces.