Originally Posted By: paul
lets add up all the forces that apply.
as the air is escaping from the tank.

the ends of the tank

114.7 psi --->
114.7 psi <---

Pressures are potential energy; as in stored energy. You cannot use them directly to determine the force generated upon the release of that pressure. After all, the same 100psi pressure difference with 1000cuft of air has a lot more stored energy than does 1cuft at the same pressure.

Pressure, in this case, is transformed into into momentum thourgh two "conversion" processes. The first is through accelerating the air, giving it kinetic energy. The second is through the expansion of the gas as it leaves a tank - a properly designed nozzle can harness that expansion energy and produce thrust above what the kinetic energy of the air alone provides. The exact amount of force produced is determined by:

F=[m*Ve]+[(Pt-Pa)*Ae], where

m = mass of gas
Ve = exhaust velocity (speed material leaves tank)
(Pt-Pa) = pressure difference between tank and air
Ae = area of nozzle the are is escaping through

You may have noticed that in the above formula you're essentially calculating F(total) = F(from kinetic energy of air) + F(from pressure differential)

In your example we can fill in a few numbers. A cuft of air weights approx 34g, so 1000cuft weights 34,000g (34kg). Your pressure difference is 100PSI, which is SI units is 6895kPa.

Ve is determined by a fairly complex formula:

This becomes more complex when you take into account the pressure decreases as the tank empties, but you get the idea.

Originally Posted By: paul
net result of force to pipe 100 psi <---

Once again, pressure is stored energy and thus cannot be used to determine the net force generated on an object. You need to calculate the force developed by the mass of the gas, combined with the differential pressure between the inside/outside of the tank to determine the force generated.

And once again, we come back to the very simple physical principal you insist on ignoring - newtons 3rd law. As the air leaves the tank, both the tank and that air experience an equal, but opposite force. This force imparts both the tank and air with an equal, but opposite, amount of momentum.

In an open system the momentum behind that air is dissipated into the surroundings.

Where do your propose it goes in your sealed pipe?

The answer, of course, is simple - the momentum of that air is transfered to whatever the air encounters. Namely, the momentum is transfered to the pipe as the air encounters the pipe. Since the momentum of the air is equal, but opposite, to the momentum of the tank, the air will impart and equal, but opposite momentum to the pipe.

One equal, plus an equal but opposite, equals zero.

A + -A = 0

Originally Posted By: paul
nothing is gained inside the pipe , nothing is lost inside the pipe except the energy that was put into compressing the air , but the pipe moves.

I would wager that the exact amount of energy that is is held in the compressed air ( due to its compression ) inside the tank is the exact amount of energy that is applied for propulsion of the pipe.

The amount of ***potential energy*** in the compressed air is the maximum amount which can be "extracted" in the form of thrust. But newtons 3rd law dictates that the force generated will act evenly on both the air coming out of the tank as well as on the tank itself. Since that escaping air is contained in the pipe, it's momentum is transfered to the pipe, thus countering the momentum the tank exerts on the pipe. Giving you a net change in the momentum of the pipe of zero.

But hey, ff you're so confident why don't you build it, patent it, and make yourself rich. After all, you've solved the single biggest problem in sending spacecraft outside of low-earth orbit - and in doing so refuted newton himself.

Or you could accept reality - you are wrong.


Edited by ImagingGeek (06/02/10 03:45 PM)