A water rocket employs a compressed gas to accelerate water through its nozzle as a means of propulsion. The water inside the motor is essentially stationary and is accelerated to the velocity at the nozzle expressed by Burnouli's equation:
Solving for Velocity:
Let this be Equation 1.The thrust is expressed by Newton's Second Law:
Where MA is the rate of change of momentum of the water being accelerated out of the nozzle.
The Mass of the fluid flowing out of the nozzle in time dt is
Where A is the nozzle area. The Momentum (mass x velocity) is, therefore
If we neglect the relatively small velocity of the water inside the motor, we can say that the momentum is gained entirely within time dt So the time rate of change of the momentum (thrust) is
by substituting for velocity from Eq. 1 above, or
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