A Unified Unsteady Modeling Framework for Blowdown Water Rocket Propulsion with Compressible Gas Discharge

Water rockets are often treated as simple demonstrations of Newtonian mechanics; however, their propulsion process involves transient liquid–gas discharge, thermodynamics, and compressible gas dynamics. This study develops a quasi-one-dimensional time-marching propulsion framework for a water rocket by separating the process into liquid- and gas-propellant phases. The liquid phase incorporates internal propellant acceleration effects, whereas the gas phase accounts for compressible discharge with choked and unchoked regimes. The model is validated against previously reported thrust measurements. An effective polytropic exponent improves agreement during liquid discharge, while the specific heat ratio is used separately in nozzle-flow calculations. Compressibility is required to capture gas-phase choking and the associated discharge duration. Parametric analyses of initial pressure, liquid filling ratio, nozzle diameter, liquid density, and pressurizing-gas properties clarify trade-offs among thrust, impulse, specific impulse, and altitude. Under the selected baseline conditions, a liquid filling ratio near 30% provides the highest altitude among the one-parameter variations considered. The results also indicate that water and compressed air offer practical performance for accessible water-rocket applications. The proposed framework provides a unified engineering basis for evaluating water-rocket blowdown propulsion, the consequences of modeling assumptions, and design-variable trade-offs. Its accessible formulation also offers potential instructional applications linking propulsion theory, numerical analysis, and experimental comparison.