# How Does Viscous Force Relate to Velocity Gradient?

• Frigus
In summary, reading Transport Phenomena by Bird, Stewart, and Lightfoot will help you understand viscosity better. It will take time, but it is definitely worth it.
Frigus
How does viscous force depends upon velocity gradient?

Linearly for a Newtonian fluid.

BvU said:
Linearly for a Newtonian fluid.

Sir I want the explanation

Please explain without the use of mathematics because I want to understand the concept which I am unable understand

Hemant said:
I want the explanation
I gathered that
However, PF is not a good replacement for a textbook. Your 'no math' restriction may exclude a lot of sources, but many others remain.

What did you find so far ? Simple google brings up all kinds of useful info ... e.g. this
or wikipedia.

If I were you I'd face up to the math and ask more specific questions when stuck.A velocity gradient (isn't that math too ?) points to differing velocities inside the liquid. Faster bits of liquid will want to accelerate slower bits and slower bits will want to drag down the faster ones. I.e. transport (along the direction of the velocity gradient) of momentum in a direction perpendicular to that gradient. The liquid responds with resistance: a kind of friction.

Your question cannot be answered without mathematics since only with math one can explain what viscosity is. A very vague non-mathematical definition is that it is a transport coefficient that describes the dissipative transport of momentum.

Delta2
BvU said:
I gathered that
However, PF is not a good replacement for a textbook. Your 'no math' restriction may exclude a lot of sources, but many others remain.

What did you find so far ? Simple google brings up all kinds of useful info ... e.g. this
or wikipedia.

If I were you I'd face up to the math and ask more specific questions when stuck.A velocity gradient (isn't that math too ?) points to differing velocities inside the liquid. Faster bits of liquid will want to accelerate slower bits and slower bits will want to drag down the faster ones. I.e. transport (along the direction of the velocity gradient) of momentum in a direction perpendicular to that gradient. The liquid responds with resistance: a kind of friction.

Sir as I can understand velocity gradient is change in velocity with depth

If I am not wrong then when we move from from bottom to top,if then velocity gradient gradient is more then if we move from bottom to top a large diffference in the velocity will be there in comparison to fluid with less velocity gradient this means that the fluid is providing less viscous force so isn't the force should be inversely proportional to the velocity gradient

Like infinite force for a liquid that doesn't move ?
Nature tells us not: a bigger gradient means a bigger resistance

For a molecular explanation of how viscosity comes about physically with a velocity gradient, see Chapter 1 of Transport Phenomena by Bird, Stewart, and Lightfoot.

vanhees71 said:
Your question cannot be answered without mathematics since only with math one can explain what viscosity is. A very vague non-mathematical definition is that it is a transport coefficient that describes the dissipative transport of momentum.

Sir
Chestermiller said:
For a molecular explanation of how viscosity comes about physically with a velocity gradient, see Chapter 1 of Transport Phenomena by Bird, Stewart, and Lightfoot.

Sir but at a time how can I but a book

BvU said:
Like infinite force for a liquid that doesn't move ?
Nature tells us not: a bigger gradient means a bigger resistance
Can you elaborate more

Hemant said:
Sir

Sir but at a time how can I but a book
I don't understand what you are asking. Do you not have access to a library or are unable to order books from Amazon?

Chestermiller said:
I don't understand what you are asking. Do you not have access to a library or are unable to order books from Amazon?
Sir I don't have enough time(as I am studying for competitive exam) to read a book for understand only fluid mechanics.

Hemant said:
Sir I don't have enough time(as I am studying for competitive exam) to read a book for understand only fluid mechanics.
I didn't tell you to read the whole book. The information you want is in Chapter 1

Chestermiller said:
I didn't tell you to read the whole book. The information you want is in Chapter 1
Sir I am in 11th standard,
So I want to know that if I read will be I be able to understand it with my level and also how much time will be needed to read this chapter.

Hemant said:
I don't have enough time

So you would like us to spend our time typing in what can be easily found in a book? Exactly how much more valuable is your time than ours?

You got some very good advice in this thread. I think you should take it.

vanhees71
So you would like us to spend our time typing in what can be easily found in a book? Exactly how much more valuable is your time than ours?

You got some very good advice in this thread. I think you should take it.

Sorry sir,
I don't meant to say what you have understood.

As sir said I have to read book(as per him I have to read a chapter) but I thought that for fluid mechanics I have to read full book but for students like me preparing for competitive exam have to cover these topics in short time (of about 15 days) in which we also have to do a lot objective question.

You should read the chapter if you want to learn this. No matter how much time it takes.

You should read the chapter if you want to learn this. No matter how much time it takes.
Ok sir I will.

You should not simply "read" physics books but work with them, i.e., as a first step you should sit down with pencil and paper and work out everything what's written in the text and derive everything such that you really understand it. Then you should do many problems. Last but not least, you should find some other students in your course to learn together and discuss the material. Don't do this just a few days before some exam. Exams are just to give you feedback on how well you really understood the material. The real goal should be to understand the science. As Peebles rightly said yesterday in the Nobel interview when asked for advice for young students: You should study science, because you are interested in it!

vanhees71 said:
You should not simply "read" physics books but work with them, i.e., as a first step you should sit down with pencil and paper and work out everything what's written in the text and derive everything such that you really understand it. Then you should do many problems. Last but not least, you should find some other students in your course to learn together and discuss the material. Don't do this just a few days before some exam. Exams are just to give you feedback on how well you really understood the material. The real goal should be to understand the science. As Peebles rightly said yesterday in the Nobel interview when asked for advice for young students: You should study science, because you are interested in it!

Thanks sir

## What is Newton's law of viscosity?

Newton's law of viscosity is a scientific principle that describes the relationship between the shear stress and shear rate of a fluid. It states that the shear stress of a fluid is directly proportional to the shear rate and the proportionality constant is known as the viscosity of the fluid.

## What is the difference between Newtonian and non-Newtonian fluids?

Newtonian fluids are those that follow Newton's law of viscosity, meaning their viscosity remains constant regardless of shear rate. Non-Newtonian fluids, on the other hand, do not follow this law and their viscosity can change depending on the shear rate.

## How is viscosity measured?

Viscosity is typically measured using a viscometer, which is a device that applies a known shear stress to the fluid and measures the resulting shear rate. The viscosity can then be calculated using Newton's law of viscosity.

## What factors can affect the viscosity of a fluid?

The viscosity of a fluid can be affected by factors such as temperature, pressure, and the presence of additives. In general, an increase in temperature can decrease the viscosity of a fluid, while an increase in pressure can increase the viscosity. Additives can also alter the viscosity of a fluid by changing its molecular structure.

## Why is Newton's law of viscosity important?

Newton's law of viscosity is important because it helps scientists and engineers understand and predict the behavior of fluids. It is also essential in many industrial processes, such as the production of food, cosmetics, and pharmaceuticals, where the viscosity of fluids plays a crucial role in their quality and performance.

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