Originally Posted By: paul
I already have shown you , bonehead.

the q*ve = a sum
then you add that sum to the


And that is different from my formula how? The plus is in there - are you blind, or just stupid?

Originally Posted By: paul
F = q Ve + (Pe - Pa) Ae

you are leaving out one of the sums.

No, I am not. m*Ve is zero when you do not have a nozzle which allows for expansion. Ergo m*Ve will always be zero in the case of your perpetual motion machine, as you specified the air was coming out of a tube - as in a non-divergent nozzle.

0 + anything is the same as anything by itself...

Originally Posted By: paul
There are two sources of force that move the pipe

true , ..... it just so happens that you are leaving
one of them out !!!

so when you add them together your answer is incorrect
because one of them is zero.

I did not leave one of them out - I provided you with the formula for Ve, and in the case you have described it's value will be zero. Don't take my word for it - do the math for yourself.

Without a divergence cone Po = Pe. No matter how much you try and deny it, having a Po and Pe which are the same means Ve is zero. Basic math.

Originally Posted By: paul
the pressure differential and the expansion of the gas once it leaves the pipe (captured by the nozzle).

Wrong ... the pressure differencial and the expansion are
the (Pe-Pa)*Ae side of the formula...

Nope. (Pe-Pa)*Ae refers to the pressure differential between the pressurized tank and the outside environment. Ve is determined by the pressure differential in the stream of gas as it expands once it leaves the tank and enters the nozzle.

A primer on these calcs:

More specifically:
"If the pressure ratio (and thus expansion ratio) is 1, then F = 0. The only thrust produced by such a nozzle is the pressure thrust, or Ftotal = (Pe-Pa)Ae. Such a nozzle, of course, would have no divergent portion, since A*/Ae=1, and would be a badly designed rocket nozzle!"

Originally Posted By: paul
Originally Posted By: ImagingGeek
Momentum, BTW, is a specific physical quantity equal to mass * velocity.

so why did you leave out Momentum , mass * velocity

Because that's not what m*Ve is. m (q in your case) is the mass flow rate - as in kg/s, not the mass (as in kg alone). Hence, that portion of the formula calculates the force - not momentum - produced.

That should be self-evident to an "expert" such as yourself - you cannot summate a momentum and force, as the units (and what they describe) are different. The fact you seem to think you can summate different units of measure doesn't exactly help your credibility - not that you have any left that is.

Momentum = mass * velocity = kg*m/s
Force (in simple terms) = mass * acceleration = kg*m/s^2
Force (in m*Ve) = kg/sec * m/sec = kg*m/s^2


EDIT: I'm off to the cottage for three days. Maybe use that time to read through Richards pages and learn a little about how rockets generate thrust. Then maybe we can have a conservation that extends beyond me trying to explain simple formulas to you.

Edited by ImagingGeek (06/04/10 06:17 PM)