# Journal References

“Hydrodynamics and Thrust Characteristics of a Water-Propelled Rocket” divides the water rocket volume into two parts: air and water[1]. By applying the Free body diagram, neglecting the force of air drag, the total reaction force is expressed as:

$R_{y} = V_{e}{\dot{m}}{e} - m{w}g$

where ${\dot{m}}{e}$ and $V{e}$  are the exit mass flow rate and velocity. By assuming it is an adiabatic system, the pressure in the air can be expressed as:

$p_{0} = p_{0i}{(\frac{V_{0i}}{V_{0}})}^{n}$

where ${\dot{m}}{e}$ and $V{e}$ are the exit mass flow rate and velocity. By assuming it is an adiabatic system, the pressure in the air can be
expressed as:

$p_{0} = p_{0i}{(\frac{V_{0i}}{V_{0}})}^{n}$

where $p_{0i}$ and $V_{0i}$ are the initial air pressure and volume. The paper calculates using relative data, and tests the theoretical analysis using two pressures at two initial water heights. In addition, this paper also takes temperature data, pressure data and force data into consideration.

“Hydrodynamics of a water rocket” uses mass, momentum and energy analysis to build a model [2] . It uses this model to calculate the maximum height the water rockets can reach and find out the optimum water volume.

Different from other articles, “A novel approach for optimizing Two-Phase Flow in Water Rockets” uses energy balance analysis to find the mass ratio of water and gas [3]. The energy equation is characterized by:

$\frac{1}{2}\left( m_{w} + m_{g} \right)V_{\text{eq}^{2}} = (h_{\text{ig}} - h_{\text{eg}})m_{g}$

Additionally, this article makes a chart showing the relationship between mass ratio, initial pressure, and equivalent velocity.

“Theoretical and experimental analysis of the physics of water rockets” checks the formula they obtained with the field test and studies the relationship between the height, velocity of the water rocket and the launching angle [4]. This article also points out new aspects of flow like the inertial effects of water in the rockets and exit of remaining air in the water rockets.

“A more thorough analysis of water rockets: Moist adiabats, transient flows, and inertial forces in a soda bottle” considers several aspects that are neglected in the above articles [5]. It finds that fog will form when the water bottle launches. The water condensation is an exothermic process and it will also contribute to the thrust. Here, the flow of water is high not just at the nozzle, but also inside the rocket.

## Works Cited

[1] Thorncroft, Glen E., Ridgely, John R., Pascual, Christopher C. 2009. Hydrodynamics and Thrust Characteristics of a Water-Propelled Rocket. International Journal of Mechanical Engineering Education. Pp.241-261.

[2] Prusa, Joseph M.. 2000. Hydrodynamics of a Water Rocket. SIAM Review. Vol. 42, No. 4, pp. 719–726.

[3] Al-Qutub, Amro, Taleb, Jad, M. A. Mokheimer, Esmail. 2013. A Novel Approach for Optimizing Two-Phase Flow in Water Rockets: Part I. Arabian Journal for Science and Engineering. Volume 39, Issue 4, pp 3169–3180

[4] Barrio-Perotti, R.; Blanco-Marigorta, E.; Fernandez-Francos, J.; Galdo-Vega, M. 2010. Theoretical and experimental analysis of the physics of water rockets. European Journal of Physics. Vol. 31, pp1131-1147.

[5] Gommes, Cedric. 2010. A more thorough analysis of water rockets: Moist adiabats, transient flows, and inertial forces in a soda bottle. American Journal of Physics. Vol.78, Pp 236-243.

[6] De Podesta, Michael. 2007, June. A guide to building and understanding the physics of water rockets. National Physical Laboratory.