A toy water rocket: Water flows from a garden hose, through a valve, and into a...

Transcribed Image Text:

A toy water rocket: Water flows from a garden hose, through a valve, and into a launch pad which redirects the jet of water to exit vertically in the Earth's gravitational field. The jet hits a "rocket" of weight W which redirects the momentum of the water jet by an angle away from the vertical. At the nozzle (in the launch pad), the area of the exiting jet is A, with volumetric flowrate Q. At the rocket, assume that the magnitude of velocity does not change during redirection, and that the pressure in the water jet just below the rocket is atmospheric. Neglect viscous effects and assume uniform velocity profiles with density p. Use an arbitrary angle 0 for the analysis, unless otherwise specified. a. Draw the appropriate (steady) control volume around the "rocket" for arbitrary angle , labeling all forces and momentum fluxes. b. Derive an expression for the minimum flowrate, Qmin' to make the rocket initially lift up from the launchpad. c. Derive an expression for the steady stable height, h, as a function of the other parameters. d. From the result of part (c), calculate the height of the jet with a typical garden hose flow rate Q=0.02 m/min (i.e. around 5 gal/min), with A = 0.5 cm, p=1000 kg/m, g = 9.8 N/kg, supporting the rocket with weight W = 2 N and 0 = 90. Ao h 0 launch pad A toy water rocket: Water flows from a garden hose, through a valve, and into a launch pad which redirects the jet of water to exit vertically in the Earth's gravitational field. The jet hits a "rocket" of weight W which redirects the momentum of the water jet by an angle away from the vertical. At the nozzle (in the launch pad), the area of the exiting jet is A, with volumetric flowrate Q. At the rocket, assume that the magnitude of velocity does not change during redirection, and that the pressure in the water jet just below the rocket is atmospheric. Neglect viscous effects and assume uniform velocity profiles with density p. Use an arbitrary angle 0 for the analysis, unless otherwise specified. a. Draw the appropriate (steady) control volume around the "rocket" for arbitrary angle , labeling all forces and momentum fluxes. b. Derive an expression for the minimum flowrate, Qmin' to make the rocket initially lift up from the launchpad. c. Derive an expression for the steady stable height, h, as a function of the other parameters. d. From the result of part (c), calculate the height of the jet with a typical garden hose flow rate Q=0.02 m/min (i.e. around 5 gal/min), with A = 0.5 cm, p=1000 kg/m, g = 9.8 N/kg, supporting the rocket with weight W = 2 N and 0 = 90. Ao h 0 launch pad