[AllAroundTheWorld]

Dude, I used to also be an Aerodynamicist for Airbus. I helped design aircraft like the A380 and A340. I know what friction is.

Shit! You could have told me before, I've flown in an A380. I'm surprised the thing didn't fall apart

Admittedly you seem to have more knowledge about all this than me but if the atmosphere was a brake on the earth in the way I think you're implying then you'd have 1000 mile an hour winds at the equator rubbing against the ground. But we don't, so...

[Dr David Thork]

Yeah, I already told you that. And relativity ...


Also, if I gave you the equation for momentum ... you'd be happy with p = m* v

However when looking at momentum of air for in-compressible air the equation for momentum needs to be expanded to



With compressible I need to expand again.

I can do the same with the drag equation.

https://en.wikipedia.org/wiki/Drag_equation

You'd be happy with


But that doesn't include relativity.

You ending up with 1000 miles per hour is the trap I set. The delta is actually only the slowing caused by friction. Say 5 mph in a light wind. V is exponential ... V^2 so you'd have been a million miles away scratching your head.

Like I said, we are done with this thread. The fun has been sucked out of it.

[BillO]

Yeah, I already told you that. And relativity ...


Also, if I gave you the equation for momentum ... you'd be happy with p = m* v

However when looking at momentum of air for in-compressible air the equation for momentum needs to be expanded to



With compressible I need to expand again.

I can do the same with the drag equation.

https://en.wikipedia.org/wiki/Drag_equation

You'd be happy with


But that doesn't include relativity.

You ending up with 1000 miles per hour is the trap I set. The delta is actually only the slowing caused by friction. Say 5 mph in a light wind. V is exponential ... V^2 so you'd have been a million miles away scratching your head.

Like I said, we are done with this thread. The fun has been sucked out of it.

What??!!!

That equation has absolutely nothing, and I mean nothing, to do with momentum.  What you have done, but are ill equipped to realize it, is to show someone else' derivation of the density distribution through an incomprehensible fluid from the mass continuity equation.  the character 'ρ' in that equation is 'rho', meaning density, not 'p' for momentum.

You have not even completed the derivation.  It needs to be set = to zero (as density is assumed not to vary over time in the applicable case) to give a partial differential equation which then needs to be solved.

You're out of your depth man.

[Round Eyes]

Yeah, I already told you that. And relativity ...


Also, if I gave you the equation for momentum ... you'd be happy with p = m* v

However when looking at momentum of air for in-compressible air the equation for momentum needs to be expanded to



With compressible I need to expand again.

I can do the same with the drag equation.

https://en.wikipedia.org/wiki/Drag_equation

You'd be happy with


But that doesn't include relativity.

You ending up with 1000 miles per hour is the trap I set. The delta is actually only the slowing caused by friction. Say 5 mph in a light wind. V is exponential ... V^2 so you'd have been a million miles away scratching your head.

Like I said, we are done with this thread. The fun has been sucked out of it.

What??!!!

That equation has absolutely nothing, and I mean nothing, to do with momentum.  What you have done, but are ill equipped to realize it, is to show someone else' derivation of the density distribution through an incomprehensible fluid from the mass continuity equation.  the character 'ρ' in that equation is 'rho', meaning density, not 'p' for momentum.

You have not even completed the derivation.  It needs to be set = to zero (as density is assumed not to vary over time in the applicable case) to give a partial differential equation which then needs to be solved.

You're out of your depth man.

Baby Thork, we are still best friends...but come on man.  you boofed this one up good.  BillO is completely right.  this is a derivation of the mass continuity equation assuming newtonian fluids...

will give you the benefit of the doubt and hopefully you just posted the wrong image.

[Dr David Thork]

Really. The Navier Stokes equations have nothing to do with momentum?

https://en.wikipedia.org/wiki/Derivation_of_the_Navier%E2%80%93Stokes_equations

Oh, look ... you start deriving them from the basic momentum equation.

Completed the equation? It was complete for the bit I described. Sure you can continue to find other things as the wiki link no doubt told you. But you had no idea what that equation even was. Its been 20 years since I had to derive that from first principles in a uni exam. No way I could derive it now. I suppose you can just derive Navier Stokes equations off the top of your head?

Even at work I never had to derive it. Each part was broken up into a separate set of programs. I just picked the program I needed and ran the numbers ... I'm wasting my time.

You have not even completed the derivation.  It needs to be set = to zero (as density is assumed not to vary over time in the applicable case) to give a partial differential equation which then needs to be solved.

You can read a wiki page and almost understand it. Nice.

You're out of your depth man.

[BillO]

Really. The Navier Stokes equations have nothing to do with momentum?

That is not what I said, is it?  What you passed off was not the Navier-Stokes equation.  It was this: https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations#Continuity_equation_for_incompressible_fluid  Which again has nothing to do with the momentum - but it can be useful in deriving the Navier Stokes equation if you re-arrange, set to zero (as is shown in the link), and then solve the resulting partial differential equation.

https://en.wikipedia.org/wiki/Derivation_of_the_Navier%E2%80%93Stokes_equations

Oh, look ... you start deriving them from the basic momentum equation.

Which you did not show

Completed the equation? It was complete for the bit I described. Sure you can continue to find other things as the wiki link no doubt told you. But you had no idea what that equation even was. Its been 20 years since I had to derive that from first principles in a uni exam. No way I could derive it now. I suppose you can just derive Navier Stokes equations off the top of your head?

Even at work I never had to derive it. Each part was broken up into a separate set of programs. I just picked the program I needed and ran the numbers ... I'm wasting my time.

You have not even completed the derivation.  It needs to be set = to zero (as density is assumed not to vary over time in the applicable case) to give a partial differential equation which then needs to be solved.

You can read a wiki page and almost understand it. Nice.

Nice try.

You're out of your depth man.

As to your recent assertion that:

Completed the equation? It was complete for the bit I described.

  No, it wasn't - again, nothing to do with momentum and not useful to Navier-Stokes derivation without solving the differential equation.

Speaking of using wiki, you obviously copied your equation directly from Wikipedia.

[Dr David Thork]

I just lost another 14 IQ points reading your post.

If you want to learn what Navier Stokes equations are for ... go do it. There is no way I'm explaining it to you and correcting you through every step when I see your errors.

[garygreen]

However when looking at momentum of air for in-compressible air the equation for momentum needs to be expanded to

did they not teach you dimensional analysis at uni?

both sides reduce to kg s^-1.  this is not a momentum equation.  it's a mass flow equation.

all this is saying is that for an incompressible fluid, you can't have sources or sinks of mass due to fluid flow.