Air expansion in the water rocket

TL;DR

This paper investigates the thermodynamics of water rocket thrust, modeling air expansion with vapor effects, and validates a polytropic process approximation through experiments and analytical derivation.

Contribution

It introduces an analytical expression for the polytropic index based on initial conditions, validated by experimental data.

Findings

Air expansion follows a polytropic process with parameter β.

Analytical expression for β matches experimental results.

Thermodynamic model includes vapor effects and environmental energy exchange.

Abstract

We study the thermodynamics of the water rocket in the thrust phase, taking into account the expansion of the air with water vapor, vapor condensation and the energy taken from the environment. We set up a simple experimental device with a stationary bottle and verified that the gas expansion in the bottle is well approximated by a polytropic process $PV^\beta$= constant, where the parameter $\beta$ depends on the initial conditions. We find an analytical expression for $\beta $ that only depends on the thermodynamic initial conditions and is in good agreement with the experimental results.