[Physics Class Notes] on Turbulence Flow Pdf for Exam

Do you know what turbulent means? Well! Turbulent Flow is the rough or a chaotic movement of fluid through a region.

Chamoli Glacier Burst led to a haphazard flow of water inside the city; this haphazard flow of water is the turbulent flow. So, the turbulent water is full of fluctuations whose speed varies at every point in terms of magnitude and direction.

However, in Physics, we will understand what is turbulent flow and the turbulent flow equation as well.

What is Turbulent Flow?

In the brief introduction to the meaning of turbulent flow, we understand that turbulent water or fluid turbulence is an irregular fluctuation or mixing of two or more liquids. 

Here, the fluid movement is in such a way that at every point, the speed of the liquid undergoes continuous variations in both magnitude and direction.

So, the rough movement of the fluid at every point is the cause of these fluctuations, that’s why we call the water turbulent water.

Point to Note

One must note that for a turbulent flow, the speed of water should be high. If it gets low, the flow becomes a smooth or non-turbulent flow. 

A Must Note

The turbulence concept is considered the last unsolved problem of Classical Mathematical Physics. 

What is Turbulent in Fluid Mechanics?

The concept of turbulence flow is straight-forward. Just look at the image below to understand it visually:

(Image to be added soon)

This image clearly shows the difference between a turbulent flow and a non-turbulent flow.

There is a term called Reynold’s number that helps us to elaborate on the turbulent flow equation. 

So, What is Reynolds Number?

A Reynolds number helps us determine whether the flow is laminar or turbulent. It is the ratio of internal forces to the viscous force. 

Now, let’s understand the Reynolds number concept through the Turbulent Flow Equation:

Turbulent Flow Equation

The equation is as follows:

Re = (⍴?D) /?

Here,

⍴ = Fluid Density in Kgm-3

?  = Kinematic viscosity in m2s-1

D = Characteristic Linear Dimension  

? = Dynamic viscosity in Pa.s

A low value of Reynolds number (Re) means that if the viscous forces of liquid are more than internal forces in a fluid, i.e., a liquid carries a low Reynolds Number or Re, the liquid is sufficient to align all its particles inline, and therefore, the flow becomes laminar. However, a higher Reynolds number means the flow is turbulent.

We can rewrite the equation (1) in the following manner:

                      Re = (⍴?D) /? = VD/?

Here, 

V  = Flow velocity in m/s

? = Kinematic viscosity, which is given by

? = ?/⍴

Transition From Laminar Flow to Turbulent Flow

For turning the laminar flow of fluid to turbulent, Reynolds number with respect to x should exceed Rex ∼ 5,00,000.

The turbulence may occur before the above range, depending on the roughness of the surface or a region through which water flows. Also, the turbulent boundary layer thickens quickly than the laminar boundary layer because of the increased shear stress at the body surface.

Turbulent Velocity

In a turbulent flow, there is varying empirical velocity at every point. The simplest and the best-known velocity profile is the power-law velocity profile. 

The velocity profile in turbulent water flow is flatter in the central part of the pipe, which is the turbulent core than in the laminar flow of the fluid. The flow velocity drops sharply when extremely close to the walls. This is because of the diffusivity of the turbulent flow. It has the following graph:

(Image to be added soon)

Here, you can see that the rise in the velocity of the fluid shows turbulent flow, while the drop in velocity shows that the flow is laminar.

Turbulent Flow in Everyday Life

1. If you have seen the windmills in your area, then you are close to the concept of turbulent flow.

2. A high-speed turbulent airflow leads to the movement of windmills, which, in turn, generates electricity that we get in our homes.

3. A turbulent water flow leads to the rotation of turbines and this rotatory motion produces electricity. The turbulent flow concept has helped us in performing daily chores during nights. 

4. Oil transport in pipelines is a turbulent flow.

5. The pipeline gas system has relieved us from standing in a queue for purchasing cylinders. This is possible because of the turbulent flow of gas to our kitchens.

6. Blood flow in our arteries is a turbulent flow.

7. We have all heard a story since our childhood that magma is generated by the internal heat of the planet or moon and it erupts as lava at volcanoes. Here, the lava flow is turbulent. 

8. An aircraft lifts its wings because of the dynamic lift. Here, dynamic lift occurs because of the pressure difference between the upper and lower airflow, which is the turbulent airflow.

9. Smoke emitting from a cigarette is a turbulent flow.