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:


(Eq. 1)

The thrust is expressed by Newton's Second Law:
Where
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
So the time rate of change of the momentum (thrust) is
by substituting for velocity from Eq. 1 above, or
