Teaching Compressible and Incompressible Fluid Dynamics and Thermodynamics from a Bottle Rocket Experiment*

A water bottle rocket test stand, coupled with a numerical model, can provide unique insights into fluid mechanics and thermodynamics. The bottle rocket test stand is designed to secure the bottle in a vertical position. A load sensor measures the net thrust force as a function of time. The net thrust force is the dynamic weight of the bottle rocket subtracted from the thrust. A pressure transducer feeds through the rocket nozzle to measure the bottle pressure as a function of time.

A numerical model is developed to predict the dynamic net thrust force based on the initial bottle pressure, water volume, and system temperature. A 4th-order Runge-Kutta method is used to calculate the change in mass over time. The pressure at each time-step is calculated with isothermal and isentropic ideal gas relationships. The velocity for the water jet is calculated using a Bernoulli energy balance, and the velocity for the air jet is calculated for both choked and subsonic flow.

The numerical model matched the measured data with less than 10% error. It was observed that a choked flow assumption, even past the choked pressure ratio, aligned well with the data. It was also discovered that an isothermal assumption for the ideal gas pressure relationship fit better than an isentropic assumption.