How Water Rockets Work
A water rocket works using the same principles as other rockets. There are three main forces in action: thrust (Fapp), drag (Ffr) and weight (w=mg). The water, which is forced out by the difference between internal and atmospheric pressure, is a reaction mass that provides the thrust. All rockets have a reaction mass, which can vary from hot gasses that are expelled when a fuel is burnt (in the Space Shuttle's SRB's for example) to water in a water rocket. The air molecules moving along the side of the rocket as it is moving create friction and result in the drag force (the drag attempts to slow the rocket down and so acts in the opposite direction as the velocity of the rocket). Weight is simply the mass of the rocket multiplied by gravity and applies to all objects within a gravitational field. Again, this force works against the rocket’s thrust, trying to bring the rocket back down to Earth. [pic]
Free body diagram of a rocket during the thrust phase
Free body diagram of a rocket during the coast phase
There are two components in the ‘fuel’ of a water rocket; water and air. Water, an incompressible fluid, is poured into the rocket before it is placed on the launcher and acts as the reaction mass. The air, which stores much more energy than the water because it is compressible (water is essentially incompressible and so pressurising a rocket adds no energy to the water), is then pumped in and pressurised; therefore the greater the pressure, the greater the energy stored. When a water rocket is launched, the difference between internal and atmospheric pressures forces the rocket off the pressure seal, followed by the expulsion of water and air out of the nozzle until the internal and atmospheric pressures are equalised. This action creates a downward force and, by applying Newton’s Third Law of Motion, it can be shown that in order for the total momentum of the system to remain constant and equal to zero (i.e. the law of conservation of momentum is not broken), there must be an equal but opposite force upon the rocket (pushing it upwards); this is the thrust, which causes the acceleration of the rocket according to the equation F=ma. A correct balance between the volumes of water and air must be found because the air stores the bulk of the energy inside the rocket. If the water volume is too high compared to the air volume, too little energy will be stored (since, as previously stated, water does not store energy inside the rocket; the air does). On the other hand, if there is too little water the reaction mass will be insufficient to provide much acceleration, since air is far lighter than water and so, again, the performance of the rocket will be less than optimum. Experimentally, a water-to-air ratio of 1:2 (one third of the volume is water) has been found to generally be the most efficient. The ejection of water and pressurised air typically takes no more than a few tenths of a second. This rapid action leaves little time for any thermal energy transfer through the walls of the bottle, thus the reaction is an adiabatic expansion. Simulations indicate that the air temperature can drop to as low as –100°C. In simulations there are typically 3 regions within the thrust phase. The first of these is the water region, where water is expelled from the nozzle in a column. The third and final region is the air region, which occurs after all of the water has been ejected and the remaining air in the pressure vessel is expelled until the internal pressure reaches the atmospheric pressure. The second region is the transition between the water and air regions, and is characterised by a mixing of the water and air. The water is ejected in a column from the nozzle as it is incompressible, however the air expands in all directions due to its compressibility. This expansion means that the second region (the transition, when the water and air mix) is clearly visible as a sort of cloud of...