Theoretical and experimental analysis of the physics of water rockets

Abstract

A simple rocket can be made using a plastic bottle filled with a volume of water and pressurized air. When opened, the air pressure pushes the water out of the bottle. This causes an increase in the bottle momentum so that it can be propelled to fairly long distances or heights. Water rockets are widely used as an educational activity, and several mathematical models have been proposed to investigate and predict their physics. However, the real equations that describe the physics of the rockets are so complicated that certain assumptions are usually made to obtain models that are easier to use. These models provide relatively good predictions but fail in describing the complex physics of the flow. This paper presents a detailed theoretical analysis of the physics of water rockets that concludes with the proposal of a physical model. The validity of the model is checked by a series of field tests. The tests showed maximum differences with predictions of about 6%. The proposed model is finally used to investigate the temporal evolution of some significant variables during the propulsion and flight of the rocket. The experience and procedure described in this paper can be proposed to graduate students and also at undergraduate level if certain simplifications are assumed in the general equations.

Cohetes hidráulicos con videos en cámara lenta

“…La solución de esta ecuación queda determinada por la relación funcional que describe el drag (F drag ), el cambio de masaṁ en función de la densidad del fluido dentro del cohete debido a los cambios de presión. La solución a este problema ha sido ampliamente abordado en la literatura,empleando diferentes métodos de análisis [1][2][3][4]13,14,[21][22][23][24][25][26][27][28][29][37][38][39][40][41][42][43].…”

“…Una revisión bibliográfica refleja una vasta literatura disponible, que describe el movimiento del cohete bajo distintas consideraciones físicas [1][2][3][4][21][22][23][24][25][26][27][28][29], sin embargo, en ningún trabajo se presenta un análisis cinemático bi-dimensional de este sistema a partir de datos experimentales a una resolución de tiempo del orden de mili-segundos Con la aparición de las cámaras fotográficas digitales de alta velocidad, es posible grabar objetos en movimiento en vídeo a velocidades superiores a los 25 fps ("cuadros por se-gundo", por sus siglas en ingles). Con la ayuda de software especializado como "Tracker" [30], se pueden analizar estas grabaciones y obtener información física del movimiento de dicho objeto [31][32][33][34][35].…”

Optimization of a Water Rocket in OpenMDAO/dymos

“…This simplied modelling can be found in Prusa [5]. A more rigorous formulation, which drops all these simplifying assumptions can be found in Wheeler [6], Gommes [7], Barrio-Perotti et al [8]. Assumption 1 is known to underestimate the rocket performance, since the air left in the bottle after it is out of water is known to generate appreciable thrust [9].…”

“…(4) from the water engine model, and fed into the ight dynamic equations eqs. (5) to (8). It starts at launch and nishes when the water is depleted, i.e.…”

On the approximation of D.I.Y. water rocket dynamics including air drag

“…[3, p. 1138]. In [3], the air propulsion is also described by a system of differential equations, see [3, eq. 29, 30, 31] together with the algebraic equation [3, eq.…”