Water Rocket - Predicting Peak Height

Predicting Peak Height

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 follows:

( = peak height reached, = Initial mass of water only, = Rocket mass with water, = Initial gauge pressure inside rocket, = density of water, = acceleration due to gravity) 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).

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