Pyrotechnic rockets, pyro for short, have engines with a fused time delay parachute release charge on top of the engine. Water rockets do not.
Water rockets' most challenging science is the recovery system. Different recovery systems listed here are better explained in other sites. See the links page.
Recovery systems require a a way to sense the event to release the recovery parachute, or streamer, or wings. And the recovery system has to eject the recovery object into the air stream to control the descent of the rocket.
Every recovery release system has parameters of operation. Consider how a flap inserted into the air flow will be held by that air flow. The rocket typically slows down near apogee. Then the airspeed flap is about balancing the forces to release the recovery device once the rocket slows. Be aware that sometimes the rocket does not slow as expected.
Wind-up devices can be used to release or to pull. Search for Tommy wind-up releases for more details. Experiement with how the timer releases the recovery device. Careful adjustment to the system should yield higher reliability.
Analog or digital, a timed event can be programmed or adjusted with an RC circuilt. The water rocket doesn't fly very long. Three seconds to apogee is a good flight. Make sure you store plenty of energy to release the recovery system.
High power pyro rockets have electronic apogee sensors to record the flight and to release the recovery system. You can lower your cost by choosing sensors that do not have the datalogger.
Find a way to push the nosecone off. Or pull it off to the side. The release has to have enough force to overcome the air resistance if the rocket is not slowed down near appogee.
Contest rules typically prohibit detonating a charge, like black powder. However, think of building up pressure with bicarbonate and water or vinegar.
Some nosecone releases rely on the nosecone fitting loosely. The forces on the rocket during accelleration and decelleration can easily dislodge the nosecone too early, or not at all.
Push a parachute out a side door. Just make sure you have enough force to get past the door.
Flight characteristics to consider when making a recovery system.
Rockets take off with tremendous force. You can hear it taking off with a bang! You can see it when the fins are left behind on the pad because they weren't secured to the rocket. And you should be careful to make the recovery release mechanism strong enough to withstand the 60+ G force during accelleration.
As soon as the rocket propulsion is spent, the rocket has acheived maximum velocity. That velocity and sudden lack of propulsion is like hitting the rocket in the nose. The rocket experiences sudden decelleration and anything not secure can be pulled apart. However, you can reduce the decelleration by making a sleek rocket with very little wind resistance.
You can construct rockets with straight fins to reduce the effect of rotation. But, if you do have some rotation, it easy to create 1 G force perpendicular to the rocket travel. That horizontal force tries to pull on your release mechanisms in some unusual ways.
Some rockets do not go straight up, stall, then come back down. Some have a curved flight path where the rocket never slows down very much.
Rockets attain very high speed and flying faster than 100 mph is common. Air resistance at those speeds can really push against the nosecone. Or that much air flow can tear off parts not secured.