Steam rocket in outer space - would it work?
closed as off-topic by Emilio Pisanty, stafusa, Kyle Kanos, glS, Jon Custer Aug 27 '18 at 16:32
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If the machine is closed, the water being pumped towards the front of the machine will have exactly equal & opposite momentum to the steam being emitted towards the back of the machine, no matter how hard the cycle is driven. No thrust.
Steam (nuclear) rocket engines work, and they were even considered and tested by NASA decades ago
..but your thing with catching the steam unfortunately doesn't work as intended; all of the kinetic energy from the water leaving the rocket engine is being transferred back to the spacecraft in the wrong direction, which cancels out the thrust of the rocket to zero. This has alot to do with pumping water up to the front of the spacecraft to sustain the rocket's propellant needs, not just the fact that the water/steam is hitting the inside of the spacecraft and braking it.
That water pump sending water to the front at the same rate that the rocket engine is sending it to the back is basically an equally-powerful rocket engine in the opposite direction. By not pumping the water to the front, you could move the spacecraft forward by the distance that you shift the center of mass of the spacecraft, which would happen because of the time delay between when the rocket nozzle first sends out propellant compared to the time that propellant first hits the wall at the back of the spacecraft (spacecraft gets a slow forward motion that stays constant during rocket operation). Then, the forward motion is halted exactly to zero by the corresponding time delay of the last propellant leaving the rocket nozzle until it hits the back wall