Water Rocket - peak height

Description

A water rocket is a type of model rocket using water as its reaction mass. Such a rocket is typically made from a used plastic soft drink bottle. The water is forced out by a pressurized gas, typically compressed air. Like all rocket engines, it operates on the principle of Newton’s third law of motion.

If aerodynamic drag and transient changes in pressure are neglected, a closed-form approximation for the peak height of a rocket fired vertically can be expressed as shown here.

Assumptions for the above equation: (1) water is incompressible, (2) flow through the nozzle is uniform, (3) velocities are rectilinear, (4) density of water is much greater than density of air, (5) no viscosity effects, (6) steady flow, (7) velocity of the free surface of water is very small compared to the velocity of the nozzle, (8) air pressure remains constant until water runs out, (9) nozzle velocity remains constant until water runs out, and (10) there are no viscous-friction effects from the nozzle (see Moody chart).

An independent variable that influences peak height is weight/mass. Depending on the thrust of the rocket propulsion system, a rocket requires a minimum mass to overcome the deleterious effects of drag. For example, the greater the thrust/the less the original weight of the rocket, the more weight or mass must be added to the rocket to insure maximum apogee. The mass is generally referred to as ballast. This principle is demonstrated by having a student throw a straw with and without a piece of clay attached to the 'nose’ of the straw. The straw with the greater mass will travel further, provided that there is sufficient thrust to overcome the ballast or extra mass.

Related formulas

Variables

hpeak height reached (m)
Miinitial mass of water only (kg)
MRrocket mass with water (kg)
Piinitial gauge pressure inside rocket (pascal)
ρdensity of water (kg/m3)
gStandard gravity