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Now, I have no training on rocketry, but as far as I can guess, in a
flared nozzle the vertical component of the pressure along the nozzle
provides the upward thrust.
Newton's 3rd is not about "stuff".
There are so many popular misconceptions about Newton's 3rd Law that
it is hard to know where to begin.
Newton's 3rd is not about "stuff". It is about forces. The worst
words are Action and Reaction, because those are easily
misinterpreted as things that happen, rather than simultaneous force
pairs.
The classic, "Q: How does a rocket work? A: Newton's 3rd Law" has
gotten countless students credit on exams, but is absolutely
meaningless. Everything works via N3, so it explains nothing.
A rocket works because the nozzle creates a pressure gradient. Lots
of force pushing up, external pressure at the bottom.
Now, I have no training on rocketry, but as far as I can guess, in a
flared nozzle the vertical component of the pressure along the nozzle
provides the upward thrust. The horizontal component is equal all
around, and the nozzle has to work hard not to explode, while
redirecting the hot exhaust downward, exactly the same way as the
bend in the firehose or the levitating waterjet.
A straight firehose with a non pressure reducing nozzle (the water
pressure stays constant until it has left the nozzle), basically a
pipe, connected to the hydrant would not have a backwards thrust. In
fact, the friction should produce a forward pull, causing the pipe or
hose to stretch. The reaction force is inside the fire hydrant, where
the vertical water flow from underground is turned 90 degrees.
Forces explain the changes in motion, but not all of those are
apparent. Conservation of momentum tells us that if something starts
moving one way, something else has to start moving the opposite way.
That other thing is often the earth, which is why these problems are
sometimes hard to work out.
An airplane in level flight or a helicopter hovering at a fixed
altitude are forcing a lot of air downward. If air moves downward,
what moves up? The answer is the earth, but its huge mass makes that
motion imperceptible. Later, the downward moving air hits the ground,
pushing the earth away.
When considering the entire closed system, include the earth.