The Flat Earth Society
Other Discussion Boards => Science & Alternative Science => Topic started by: timterroo on August 21, 2018, 05:26:56 PM

Some of the more well known folks here have come up the following formula for the momentum of an incompressible fluid  which is quite interesting!
(https://wikimedia.org/api/rest_v1/media/math/render/svg/67918cb29f0da2555d14100d6bb2efa0693b61e8)
I have inquired about this equation, and the folks here have generously agreed to give us a demonstration of how this works, and how it can be used in FET.
Please, I welcome your input!

There's no such thing as a fluid that cannot be compressed.

There's no such thing as a fluid that cannot be compressed.
If I have misunderstood the claim made for this formula, I apologize.
What does this formula claim to do, and how does it work?

There's no such thing as a fluid that cannot be compressed.
If I have misunderstood the claim made for this formula, I apologize.
What does this formula claim to do, and how does it work?
Well, you claimed that: "Some of the more well known folks here have come up the following formula for the momentum of an incompressible fluid" so I figured I would immediately point out that this can't possibly be the case, since there's no such thing as an "incompressible fluid".

There's no such thing as a fluid that cannot be compressed.
If I have misunderstood the claim made for this formula, I apologize.
What does this formula claim to do, and how does it work?
Well, you claimed that: "Some of the more well known folks here have come up the following formula for the momentum of an incompressible fluid" so I figured I would immediately point out that this can't possibly be the case, since there's no such thing as an "incompressible fluid".
In fluid dynamics, liquids are often treated as incompressible. If you prefer to claim that this formula is for compressible fluid, again I ask, please explain!

In fluid dynamics, liquids are often treated as incompressible. If you prefer to claim that this formula is for compressible fluid, again I ask, please explain!
Yes, in much of physics, things are treated as ideals that don't actually exist, which is why ideal gas equations are useless in reality. If this equation presupposes that we have something that doesn't actually exist, then perhaps you should wonder why anyone needs it. I'm not sure what else you're confused about.

Some of the more well known folks here have come up the following formula for the momentum of an incompressible fluid  which is quite interesting!
(https://wikimedia.org/api/rest_v1/media/math/render/svg/67918cb29f0da2555d14100d6bb2efa0693b61e8)
I have inquired about this equation, and the folks here have generously agreed to give us a demonstration of how this works, and how it can be used in FET.
Please, I welcome your input!
that is a well known derivation to a common equation. you claim to be well versed in physics, but you dont recognize it?

If you, or anyone else is unable to provide an explanation, a proof, an example, or even a brief description of the variables in play, then, by default, you accept defeat and we all move on.

If you, or anyone else is unable to provide an explanation, a proof, an example, or even a brief description of the variables in play, then, by default, you accept defeat and we all move on.
Seriously? We didn't create that, it's pretty well known. Sorry you can't follow along

If you, or anyone else is unable to provide an explanation, a proof, an example, or even a brief description of the variables in play, then, by default, you accept defeat and we all move on.
Seriously? We didn't create that, it's pretty well known. Sorry you can't follow along
Does the equation determine the momentum or is momentum the constant p in this equation? If momentum is the constant p, does the equation determine the expansion of some space as a factor of momentum? Could it be the expansion of something other than space? Like a prediction of a possible expansion at a given momentum? Does this account for time at all? If it determines momentum based on some other constant p, what is that constant, and then that opens up a whole host of other questions....

If it determines the expansion of space, are there some other factors in there that might influence space? What is U in this equation and why is the expansion linear?

that's a rho, not a p. and U here is fluid flow velocity.

that's a rho, not a p. and U here is fluid flow velocity.
OK, so it's the expansion of fluid in 3 dimensional space with respect to its density? Is it possible to calculate this over time (t)?
Oh nevermind, I see it now... it's in dp/dt.

I think I need to rephrase that,
It would be "expansion of fluid in 3 dimensional space as a factor of density with respect to time (t)".

Rho is a constant and it represents density, which is why the equation assumes an incompressible liquid, because if the liquid were compressible, then obviously its density cannot be a constant.
This is a mass continuity equation for NavierStokes equations. It's just taking all of the mass flow in the system and setting that equal to zero. Since we know a classical system obeys conservation of mass, this can be helpful in flow in/flow out problems in fluid mechanics.
https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations
I mean really you could have just reverse image searched the equation, since it was lifted from this exact Wikipedia page.

Rho is a constant and it represents density, which is why the equation assumes an incompressible liquid, because if the liquid were compressible, then obviously its density cannot be a constant.
This is a mass continuity equation for NavierStokes equations. It's just taking all of the mass flow in the system and setting that equal to zero. Since we know a classical system obeys conservation of mass, this can be helpful in flow in/flow out problems in fluid mechanics.
https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations
I mean really you could have just reverse image searched the equation, since it was lifted from this exact Wikipedia page.
I am pleasantly impressed! Thank you. I could have searched for the equation, yes. I learned much more by not searching for it, though. As I said in my rant, I'm 5 or 6 years out from having done any real serious math, and I only took one University Physics class, which I didn't complete (started my first 'real' fulltime job just then... life choices, ya know?) So, this has been great.... Also, sorry for the divergence of topic here.... back on track...
It's just taking all of the mass flow in the system and setting that equal to zero.
I don't see that in this equation, the setting it equal to zero part... dp/dt is the derivative correct? God there's something I'm forgetting about the "dt"....
Sorry for sounding so elementary... getting old sucks. :(

Rho is a constant and it represents density, which is why the equation assumes an incompressible liquid, because if the liquid were compressible, then obviously its density cannot be a constant.
This is a mass continuity equation for NavierStokes equations. It's just taking all of the mass flow in the system and setting that equal to zero. Since we know a classical system obeys conservation of mass, this can be helpful in flow in/flow out problems in fluid mechanics.
https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations
I mean really you could have just reverse image searched the equation, since it was lifted from this exact Wikipedia page.
I am pleasantly impressed! Thank you. I could have searched for the equation, yes. I learned much more by not searching for it, though. As I said in my rant, I'm 5 or 6 years out from having done any real serious math, and I only took one University Physics class, which I didn't complete (started my first 'real' fulltime job just then... life choices, ya know?) So, this has been great.... Also, sorry for the divergence of topic here.... back on track...
It's just taking all of the mass flow in the system and setting that equal to zero.
I don't see that in this equation, the setting it equal to zero part... dp/dt is the derivative correct? God there's something I'm forgetting about the "dt"....
Sorry for sounding so elementary... getting old sucks. :(
Density is a constant, therefore its derivative with respect to time is zero. I can't believe that I need to explain that to you after you repeatedly told me that "I'd be willing to bet that I've studied more math than most people here"

I don't see that in this equation, the setting it equal to zero part... dp/dt is the derivative correct? God there's something I'm forgetting about the "dt"....
Sorry for sounding so elementary... getting old sucks. :(
it's a statement about mass conservation. all this says is that if the fluid is incompressible (ie the density of the fluid doesn't change over time), then the divergence anywhere in the flow is zero. this implies that there are no sources or sinks of mass in the system.
(https://wikimedia.org/api/rest_v1/media/math/render/svg/d587ef3936b441229c327b33546cfe6ef2bfc0e5)

I don't see that in this equation, the setting it equal to zero part... dp/dt is the derivative correct? God there's something I'm forgetting about the "dt"....
Sorry for sounding so elementary... getting old sucks. :(
it's a statement about mass conservation. all this says is that if the fluid is incompressible (ie the density of the fluid doesn't change over time), then the divergence anywhere in the flow is zero. this implies that there are no sources or sinks of mass in the system.
(https://wikimedia.org/api/rest_v1/media/math/render/svg/d587ef3936b441229c327b33546cfe6ef2bfc0e5)
This is helpful, thank you.

I don't see that in this equation, the setting it equal to zero part... dp/dt is the derivative correct? God there's something I'm forgetting about the "dt"....
Sorry for sounding so elementary... getting old sucks. :(
it's a statement about mass conservation. all this says is that if the fluid is incompressible (ie the density of the fluid doesn't change over time), then the divergence anywhere in the flow is zero. this implies that there are no sources or sinks of mass in the system.
(https://wikimedia.org/api/rest_v1/media/math/render/svg/d587ef3936b441229c327b33546cfe6ef2bfc0e5)
Baby Thork would disagree :)

Since the cats out of the bag, check this thread for the history of that equation/nonsense. Page 6 of this : https://forum.tfes.org/index.php?topic=9809.msg159853#msg159853

Since the cats out of the bag, check this thread for the history of that equation/nonsense. Page 6 of this : https://forum.tfes.org/index.php?topic=9809.msg159853#msg159853
I've learned so much today, thank you!

Gases are fluids, I know of no incompressible gases.

Gases are fluids, I know of no incompressible gases.
Yes. The thread is incorrectly named. Fluids comprise liquids and gases. gases are compressible, liquids are not, generally.

Gases are fluids, I know of no incompressible gases.
Yes. The thread is incorrectly named. Fluids comprise liquids and gases. gases are compressible, liquids are not, generally.
Right, so liquids are in the set of incompressible fluids, which is why it is titled as such.

Gases are fluids, I know of no incompressible gases.
Yes. The thread is incorrectly named. Fluids comprise liquids and gases. gases are compressible, liquids are not, generally.
This is incorrect. All fluids are compressible, this includes liquid and gasses. In fact, all states of matter are compressible. There's no such thing as matter that cannot be compressed. Equations that assume an incompressible fluid do so for the sake of simplicity, not a genuine reflection of reality. Under most circumstances, most liquids will compress very little, but it's still a nonzero amount.

Right, so liquids are in the set of incompressible fluids, which is why it is titled as such.
Are you asking? seems like you are asking, not stating a fact. which is wrong BTW

Right, so liquids are in the set of incompressible fluids, which is why it is titled as such.
Are you asking? seems like you are asking, not stating a fact. which is wrong BTW
If you assume we are talking about "theory", which is what we are talking about, liquids are assumed to be incompressible  that is what the equation is demonstrating (however useless it is). Fluids are a set that contains both liquid and gas. If gases are compressible and liquids are incompressible, then an incompressible fluid is referring to liquids.

For several years I worked on the Woods Hole Oceanographic ship that carried the Alvin Submarine. In college we were always taught that water is incomprehensible. The guys who crewed the Alvin corrected me. They said that the Alvin has some compensation equipment aboard that corrects for the 1/2 percent per thousand feet that water actually compresses at depth. I was on several scientific expeditions where the Alvin was diving at 9 North on the underwater hydro thermal vents. The compensation becomes significant there.

If the difference between reality and approximation is too small to measure, would you even be able to distinguish the two? If not, then we're arguing over nothing, but if so, it hardly makes a difference because whether it's 1100 K or 1115 K, the engine in your car continues to function normally.
Assumptions such as incompressible or inviscid are useful; if they weren't, we wouldn't use them. In fact, there are many instances where we don't use them. Nondimensional analysis will tell you what assumptions are reasonable to make, and if you're completely intolerant of assumptions for whatever reason, there are other more complete equations that do not make those assumptions. They're just notoriously difficult to solve without using numerical methods.
To the OP, if you're interested in learning more about the sciences, I would start with /literally anything but/ Fluid Mechanics.