Executive Programs

Workshops

Projects

Blogs

Careers

Student Reviews

More

Informative Articles

Find Jobs

We are Hiring!

All Courses

Choose a category

All Courses

All Courses

07 May 2020

# What is the physical meaning of divergence, curl and gradient of a vector field?

Skill-Lync

Consider a ball in your hand. Now take any point on the ball and imagine a vector acting perpendicular to the ball on that point. That is your gradient in 3D. Now imagine vectors acting on all points of the ball. It would look something like this:

The red arrows perpendicular to the surface of the ball are the gradients (in 3D) of various points on the ball. If we apply gradient function to a 2D structure, the gradients will be tangential to the surface.

For a better understanding of gradient representation in 2D, consider that you are climbing a mountain. You are at a certain point on the mountain:

Now, you have to move in a certain direction to gain or lose altitude (shown in red arrows). These vector lines represent the gradients at your point of location in 2D:

Like is said before, if you are going to represent these gradients in 3D form, they will be perpendicular to the surface of the mountain.  Take a look at the images below:

In 3D form, Gradients are surface normal to particular points.

In 2D format, Gradients  tangents representing the direction of steepest descent or ascent.

## Divergence:

Consider water flowing through a large pipe. Now, it has smaller pipes joined to it. Hence, as the water flows, more water is added along the way by the smaller pipes. Hence, the mass flow rate increases as the water flows.

In another case, consider that there is a leakage in the pipe. Hence the mass flow rate decreases as it flows. This change in the flow rate through the pipe, whether it increases or decreases, is called as divergence. Divergence denotes only the magnitude of change and so, it is a scalar quantity. It does not have a direction.

When the initial flow rate is less than the final flow rate, divergence is positive (divergence > 0). If the two quantities are same, divergence is zero. If the initial flow rate is greater than the final flow rate divergence is negative (divergence <0).

## Curl:

Imagine pouring water in a cup. The water won’t just low linearly but rather, as it reaches the end of the cup, it will flow in a rotational motion before settling in the cup. Or consider water draining down the sink, it will swirl in a rotational motion before going out. If we plot this rotational flow of water as vectors and measure it, it will denote the Curl.

Curl is a measure of how much a vector field circulates or rotates about a given point. when the flow is counter-clockwise, curl is considered to be positive and when it is clock-wise, curl is negative. Sometimes, curl isn’t necessarily flowed around a single time. It can also be any rotational or curled vector.

Learning about gradient, divergence and curl are important, especially in CFD. They help us calculate the flow of liquids and correct the disadvantages. For example, curl can help us predict the voracity, which is one of the causes of increased drag. By using curl, we can calculate how intense it is and reduce it effectively. Calculating divergence helps us understand the flow rate and correct it to suit our needs.

Check out List of Job opportunities for your Engineering Domain

Author

VivekB

Author

Skill-Lync

Related Blogs

A Guide to Help FEA Engineers Get Started With Vehicle Dynamics - Part 1

Explore the fundamentals of vehicle dynamics and ultimate trends in the field from design and modeling to control with Skill Lync's exclusive course on the subject. Read about how Skill-Lync's CAE courses can help you get employed.

29 Jul 2020

How Using GT-Power in CFD Can Benefit the Automation Industry

In this article, we will briefly discuss the working, applications, and features of the one-dimensional systematic simulation tool, GT-Power, in Emission Control Strategy, engine calibration, hybrid vehicle modeling. Read about how Skill-Lync's CAE courses can help you get employed.

29 Jul 2020

Design Basics of Geometric Dimensioning and Tolerancing

This article offers a brief introduction to the globally accepted standard of Geometric Dimensioning and Tolerancing, and its importance for the entire manufacturing process. Read about how Skill-Lync's CAE courses can help you get employed.

29 Jul 2020

Chapter 5 – Going a step into Biomechanics

10 May 2020

The Basics of the Powertrain NVH: Part 2

The powertrain is the most prominent source of vibrations that affects the driving experience for the people on board. This blog from Skill-Lync examines these vibrations to help enhance that experience.

22 Aug 2020

Author

Skill-Lync

Related Blogs

A Guide to Help FEA Engineers Get Started With Vehicle Dynamics - Part 1

Explore the fundamentals of vehicle dynamics and ultimate trends in the field from design and modeling to control with Skill Lync's exclusive course on the subject. Read about how Skill-Lync's CAE courses can help you get employed.

29 Jul 2020

How Using GT-Power in CFD Can Benefit the Automation Industry

In this article, we will briefly discuss the working, applications, and features of the one-dimensional systematic simulation tool, GT-Power, in Emission Control Strategy, engine calibration, hybrid vehicle modeling. Read about how Skill-Lync's CAE courses can help you get employed.

29 Jul 2020

Design Basics of Geometric Dimensioning and Tolerancing

This article offers a brief introduction to the globally accepted standard of Geometric Dimensioning and Tolerancing, and its importance for the entire manufacturing process. Read about how Skill-Lync's CAE courses can help you get employed.

29 Jul 2020

Chapter 5 – Going a step into Biomechanics

10 May 2020

The Basics of the Powertrain NVH: Part 2

The powertrain is the most prominent source of vibrations that affects the driving experience for the people on board. This blog from Skill-Lync examines these vibrations to help enhance that experience.

22 Aug 2020

Book a Free Demo, now!

Related Courses

MATLAB Python and CFD using Solidworks for Mechanical Engineering Applications
4.7
13 Hours of content
Cfd Domain
4.7
149 Hours of content
Cae Domain
4.7
5 Hours of content
Cfd Domain
4.8
19 Hours of content
Cae Domain
4.7
3 Hours of content
Cae Domain
4.8
37 Hours of content
Cae Domain
Recently launched
2 Hours of content
Cae Domain
Recently launched
0 Hours of content
Cae Domain
Showing 1 of 13 courses