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In: Mechanical Engineering

Drag measurements were taken for a 5 cm diameter sphere in water at 20 °C to...

Drag measurements were taken for a 5 cm diameter sphere in water at 20 °C to predict the drag force of a 1 m diameter balloon rising in air with standard temperature and pressure. Given kinematic viscosity of water (v) = 1.0 X 10-6 m2/s and kinematic viscosity of air (v) = 1.46 X 10-5 m2/s.

  1. Perform the Buckingham Pi theorem to generate a relationship for FD as a function of the independent variables. Assume the drag FD is a function of diameter (d), velocity (V), fluid density (ρ) and kinematic viscosity (v)

2.Determine the sphere velocity if the balloon was rising at 3 m/s

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