A nuclear saltwater rocket is a concept for an advanced spacecraft propulsion system, proposed by Doctor Robert Zubrin. It uses water as propellant and uranium tetrabromide (a water-soluble salt) as fuel. The uranium used is enriched, between 20% and 90% 235U. This enriched uranium salt is dissolved in the water and stored in neutron-attenuating boron tubes to keep the fuel storage below critical mass.
The rocket works by injecting the fissile saltwater into a reaction plenum, creating a critical mass, which leads to a runaway nuclear reaction that heats the water, flashing it to steam and accelerating it to thousands of meters per second.
A conservative configuration using 20% 235U and managing to fission 0.1% of the fissionable fuel would yield an exhaust velocity of 69 kilometers per second, according to figures posited by Zubrin. This yields a specific impulse of around 7000 seconds, making the engine 15.5 times more efficient* than the Space Shuttle's main engines, which are in turn just about the most efficient chemical rockets possible. A ship equipped with this sort of engine, having a mass ratio of 5, which is far less than any modern spacecraft, would have enough delta-v to take off from Earth, do a Hohmann transfer to Pluto and back twice, then land on Earth again. Impressive, no?
But it gets better: If the uranium were enriched to 90% instead, and the reaction controlled to consume 90% of the fission fuel instead of 0.1% (a formidable feat, but not impossible in theory), the engine could attain an exhaust velocity of 4720 kilometers per second - greater than solar escape velocity. This translates to a specific impulse of 472 kiloseconds, or a little over a thousand times as efficient as the space shuttle. With a mass ratio of just 2.7 (that's roughly e, by the way), a ship thus equipped could fly to Mars, thrusting one gravity all the way, and still have propellant left on arrival. Enough propellant, in fact, to fly back to Earth on a brachistochrone trajectory at an acceleration of 0.1 gravities. With a larger mass ratio, such an engine might even be up to the challenges of interstellar travel.
On top of all this, the NSWR is one of the few next-generation spacecraft propulsion systems that produces both high exhaust velocity and high thrust. Indeed, it wouldn't be hard to match or even exceed the tremendous thrust possible with chemical rockets nowadays. A typical interplanetary spacecraft doesn't generally need such high thrust, but it's useful for taking off, or for vessels like warships that might need to make rapid, violent course changes.
Now, such an engine must have problems, you say, or we'd surely be rushing to build them today. Well, there are a great many problems. For one, designing a reaction chamber that can survive more than a few seconds of full-power operation is a decidedly nontrivial feat - but Dr. Zubrin thinks it can be done, and has some math to back this up. Another issue is that the rocket spews out massive quantities of incredibly radioactive exhaust with incredible force. It would leave a massive crater that will glow blue for the foreseeable future, and cause horrific radioactive contamination for dozens of kilometers around the launch site. Because of this, it's a terrible engine for takeoffs, even though its high thrust and outstanding thrust-to-mass ratio seems to make it useful for this. The radioactive exhaust is not a problem in space, however, though it does mean that there will need to be radiation shielding to protect the crew from the engine and its exhaust.
Another problem with the NSWR is that its fuel storage system is inherently unstable. If the boron isolation tubes are breached, critical mass could easily be reached, resulting in a small nuclear explosion inside the ship's fuel tank. Needless to say, this would have catastrophic results.
Still, the NSWR looks like a promising next-generation spacecraft engine, if the engineering problems can be overcome.
*Although the specific impulses given here are 15.5x and ~1000x as efficient as the SSMEs, that actually reduces the required propellant for a given amount of delta-v by much more than that. This is because as the ratio of exhaust velocity to required delta-v increases linearly, the mass ratio necessary to obtain that delta-v increases exponentially. See The Custodian's writeup on specific impulse for some examples.