Parth G | The Incorrect Assumption Made by Fluid Dynamics, and Why It Still Works - Fluids by Parth G @ParthGChannel | Uploaded 3 years ago | Updated 10 hours ago
Here's how scientists study how fluids flow!
A fluid is any substance that deforms continuallyunder shear stress. More simply, it is anything that can flow. Therefore, the term "fluid" usually refers to liquids and gases.
Fluid dynamics is an area of physics that deals with the flow of fluids. A related field is fluid statics, which studies stationary fluids. Both dynamics and statics are part of a bigger field known as fluid mechanics.
In this video, we'll be looking at the assumptions made by the theory of fluid dynamics. Every theory in physics is based on assumptions, and when these assumptions are shown to be untrue we know our theory will not apply.
Fluid dynamics is based on a few common classical physics assumptions. Specifically, we assume conservation of mass, conservation of momentum, and conservation of energy. In this video we see how conservation of mass is encoded in the mathematics of fluid dynamics, by considering a small region of space through which our fluid can flow.
The final assumption of fluid dynamics is known as the continuum assumption. This is the assumption that any fluid can be treated as a smooth continuum, rather than lots of little particles. If we look at a fluid on the large scale (or from far enough away), this assumption is reasonable as a fluid does behave as a continuum. But on the small scale, each fluid is made up of lots of atoms or molecules. If we are looking closely enough that we can "see" the particles, we need to use Statistical Mechanics instead. From further away though, the continuum assumption makes the mathematics a lot more doable and is still fairly accurate.
There is a quantity known as the Knudsen Number that allows us to calculate whether we are looking on a large enough scale such that fluid dynamics is accurate, or if we're looking at a small scale and we need to use statistical mechanics.
in this video, we also see that it is common to study each fluid by considering lots of little "fluid elements". Each fluid element has a constant mass, and we can study how it changes over time. If we consider lots of fluid elements together, we can see how an entire fluid flows over time.
Read more about fluids here (these pages are a good start):https://en.wikipedia.org/wiki/Fluid
https://en.wikipedia.org/wiki/Fluid_dynamics
https://en.wikipedia.org/wiki/Knudsen_number
Timestamps:
0:00 - Fluid Dynamics (a Branch of Fluid Mechanics)
0:30 - What is a Fluid? A Substance that Deforms Continually Under Shear Stress
2:00 - The Assumptions Made by Fluid Dynamics
3:19 - Conservation of Mass for a Fluid
4:29 - Fluids are NOT Made of Particles?! (The Continuum Assumption)
5:54 - Fluid Elements - Small Bits of Fluid with Constant Mass
6:18 - Applications of Fluid Dynamics
6:38 - What Other Aspects of Fluid Dynamics Should I Cover in a Video?
Many of you have asked about the stuff I use to make my videos, so I'm posting some affiliate links here! I make a small commission if you make a purchase through these links.
A Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
A General Relativity Book I Enjoy: https://amzn.to/3ytaKwt
My camera (Sony A6400): https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
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Gorillapod Tripod: https://amzn.to/3wQ0L2Q
Thanks so much for watching - please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
Here's how scientists study how fluids flow!
A fluid is any substance that deforms continuallyunder shear stress. More simply, it is anything that can flow. Therefore, the term "fluid" usually refers to liquids and gases.
Fluid dynamics is an area of physics that deals with the flow of fluids. A related field is fluid statics, which studies stationary fluids. Both dynamics and statics are part of a bigger field known as fluid mechanics.
In this video, we'll be looking at the assumptions made by the theory of fluid dynamics. Every theory in physics is based on assumptions, and when these assumptions are shown to be untrue we know our theory will not apply.
Fluid dynamics is based on a few common classical physics assumptions. Specifically, we assume conservation of mass, conservation of momentum, and conservation of energy. In this video we see how conservation of mass is encoded in the mathematics of fluid dynamics, by considering a small region of space through which our fluid can flow.
The final assumption of fluid dynamics is known as the continuum assumption. This is the assumption that any fluid can be treated as a smooth continuum, rather than lots of little particles. If we look at a fluid on the large scale (or from far enough away), this assumption is reasonable as a fluid does behave as a continuum. But on the small scale, each fluid is made up of lots of atoms or molecules. If we are looking closely enough that we can "see" the particles, we need to use Statistical Mechanics instead. From further away though, the continuum assumption makes the mathematics a lot more doable and is still fairly accurate.
There is a quantity known as the Knudsen Number that allows us to calculate whether we are looking on a large enough scale such that fluid dynamics is accurate, or if we're looking at a small scale and we need to use statistical mechanics.
in this video, we also see that it is common to study each fluid by considering lots of little "fluid elements". Each fluid element has a constant mass, and we can study how it changes over time. If we consider lots of fluid elements together, we can see how an entire fluid flows over time.
Read more about fluids here (these pages are a good start):https://en.wikipedia.org/wiki/Fluid
https://en.wikipedia.org/wiki/Fluid_dynamics
https://en.wikipedia.org/wiki/Knudsen_number
Timestamps:
0:00 - Fluid Dynamics (a Branch of Fluid Mechanics)
0:30 - What is a Fluid? A Substance that Deforms Continually Under Shear Stress
2:00 - The Assumptions Made by Fluid Dynamics
3:19 - Conservation of Mass for a Fluid
4:29 - Fluids are NOT Made of Particles?! (The Continuum Assumption)
5:54 - Fluid Elements - Small Bits of Fluid with Constant Mass
6:18 - Applications of Fluid Dynamics
6:38 - What Other Aspects of Fluid Dynamics Should I Cover in a Video?
Many of you have asked about the stuff I use to make my videos, so I'm posting some affiliate links here! I make a small commission if you make a purchase through these links.
A Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
A General Relativity Book I Enjoy: https://amzn.to/3ytaKwt
My camera (Sony A6400): https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Microphone and Stand (Fifine): https://amzn.to/2OwyWvt
Gorillapod Tripod: https://amzn.to/3wQ0L2Q
Thanks so much for watching - please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
