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Is Bernoulli's principle applicable in viscous liquids?

Physics Asked on July 8, 2021

I found very conflicting answers to this question.

My textbook says viscosity is neglected for the derivation but it doesn’t say anything about if it will still hold if viscosity is present.

Another reference book I have says viscosity is not an assumption for ideal fluid flow for which Bernoulli’s principle is valid.

In my opinion it is not valid since it is conservation of energy ,energy is lost due to viscous forces.

I feel I have flawed somewhere conceptually. I learn physics by myself so please go easy on me if this is a dumb question 🙂

2 Answers

You approach is correct except one thing. Ideal fluid has two properties: incompressible and has no viscosity. Apart from this what ever you said is correct. You can learn more about the viscous flows here: An equivalent for the Bernoulli equation for viscous liquids

Correct answer by Kian Maleki on July 8, 2021

For a case where the change in internal energy is small- such as a liquid flowing in a pipe- instead of using the first law of thermodynamics for a rigorous energy balance, you can add a "loss" term- sometimes called a head loss for all energy terms expressed in head- to the Bernoulli equation to account for the effects of viscosity. For example, for steady flow of liquid in a pipe of constant diameter the decrease in pressure is due to the friction loss.

The text Transport Phenomena by Bird, Stewart, and Lightfoot provides a detailed discussion. Also, you can search the web for "Bernoulli equation friction loss".

Answered by John Darby on July 8, 2021

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