Is it possible to launch a rocket with steam by using a fission reactor?

Question

The idea is to use a fission reactor to turn water into steam pumping it outside the reaction chamber through heat pipes.

Answer 1

Could you make a nuclear thermal rocket using water as a reaction mass? Sure! People have looked at that, as it would be nice to be able to refuel rockets in space from things you find (see Nuclear thermal rockets using indigenous extraterrestrial propellants)

Could you launch from Earth with such a rocket?

Well, maybe.

Would it be worth it?

Maybe not.

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Lets assume first that you can have a nuclear rocket with a sufficient thrust-to-weight ratio to get off the ground. The classic NERVA design might not have had this property, but things like Project Timberwind or DUMBO both suggested this might be possible... the latter even suggested a better thrust-to-weight than the Space Shuttle's main engines using water as reaction mass. Real world politics shelved those designs (at least in part due to ecological concerns about running an open cycle nuclear reactor in the biosphere we live in).

Anyway. I'll be pulling in some stuff from this related answer which may be of interest to you. An important figure of merit in a rocket engine is the "characteristic velocity":

$$c_* \propto \sqrt{\frac{T_t}{M_w}}$$

where $T_t$ can be taken to be the exhaust temperature, and $M_w$ is the molecular weight of the gas species in the exhaust.

Problem is that having your exhaust made up of big, heavy molecules like H₂O limits its velocity. You can counter this by increasing your operating temperature, but now you're running into problems with your engine melting.

A solid-core nuclear thermal rocket has a chamber temperature pretty similar to that of a modern hydrogen-oxygen rocket, and if your NTR runs on water then its exhaust products will be the same too, which means you end up with the same rocket performance.

We don't have any single-stage-to-orbit LH/LOX rockets. Your water-NTR would end up needing something like the Space Shuttle's arrangement of disposable boosters and a massive reaction mass tank. That's a lot of hazardous nuclear material, radioactive exhaust, untried technology and great expense for not a lot of gain! it'd be better to use a regular rocket to fly a low-thrust, high-efficiency nuclear rocket into space instead.

If you were prepared to stretch the bounds of plausibility a little, you could imagine a Closed-Cycle Gas-Core NTR which might be able to offer an efficient SSTO when fueled with water. Maybe. The engineering required to build such a thing is quite beyond us right now, and quite frankly I'd expect to see working fusion reactors and electromagnetic launch systems before anyone built a nuclear lightbulb like this.