Please help me build a rocket with water as propellant.
Here are the basic steps to build a rocket with water as propellant:

Gather materials: To build a water rocket, you'll need a plastic soda bottle (2-liter size is ideal), a cork that fits snugly in the bottle's opening, a tire valve stem, a bicycle pump, duct tape, and fins made from cardboard or plastic.

Prepare the rocket: Cut off the bottom of the soda bottle, and attach fins to the sides with duct tape. Then, insert the valve stem into the cork and push the cork into the bottle opening.

Fill the rocket with water: Fill the bottle about one-third full with water. The amount of water you use will affect the rocket's flight, so experiment with different amounts to see what works best.

Add air pressure: Use the bicycle pump to add air pressure to the rocket. The more air pressure you add, the higher the rocket will fly. Be careful not to overinflate the rocket, as it could burst.

Launch the rocket: Place the rocket on a launch pad (you can make one from PVC pipe or wood) and quickly remove the cork to release the water and air. The water will act as the propellant, pushing the rocket upward.
I meant a real one that could be used to fly outside of Earth's atmosphere, into space.
It would be quite inefficient to reach space only with a water rocket, as the ejection speed of the propellant is significantly lower than common rocket engines. However, it's possible, and the key point is superheating the water before launch to store as much energy inside as possible. The water also needs to be mixed with phase destabilisers for better conversion to steam.

The delta-v, or the maximum change in speed a rocket can achieve, to touch the space is roughly 1.5-2km/s, which is spended to overcome gravity and atmosphere drag. This is significanly lower than the 7.8km/s of delta-v to reach low earth orbit, but is still a difficult task for your water rocket. According to the rocket equation *deltav = vln(m0/mf)*, where *v* is the exhaust velocity of the rocket, m0 is the initial mass of the rocket, and mf is the dry mass, we need to reduce the weight of the water tank and increase the exhaust velocity for better efficiency. 

Now is the design part. By superheating the water in advance, as well as installing batteries and heaters inside the rocket to maintain the pressure in flight, we can get an exhaust velocity of about 800m/s. For the rocket body, we can refer to the water-propellant first stage of ARCA's EcoRocket. It has a dry mass of 360kg and an initial mass of 3930kg, which leads to a delta-v of 1.9km/s - completely suitable for our project! It is a 6.6-meters-tall and 1.2-meters-wide cylinder made of composite materials together with the heaters. Their design also tells us that a thrust-to-weight ratio of about 2:1 is enough. However, the detailed design and material is not provided, and there is a lack of other similar designs.

To build a similar rocket without enough information, you can begin with the design of a stainless steel electric boiler. The whole system needs to be scaled up to achieved the required ratio of dry mass and initial mass. Generally, the heaters can be powered by Li po batteries, and the engine can be as simple as a bell nozzle and a valve. However, you still need to consult real experts for a successful engine design.