Two early hybrid rocket tests showed that a malfunctioning rocket is indistinguishable from a bomb. Shell...

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Two early hybrid rocket tests showed that a malfunctioning rocket is indistinguishable from a bomb. Shell fragments from a zero-altitude explosion travel a distance R that can be considered a function of the following parameters: • the characteristic size L of the fragment (SI units of m), • the available combustion energy E within the chamber (SI units of J), • the rocket casing density p (SI units of kg/m3), • the local gravitational acceleration g (SI units of m/s2), • the atmospheric kinematic viscosity v (SI units of m2/s), and • the atmospheric sound speed a (SI units of m/s). (a) How many dimensionless groups are necessary to describe this problem, and why? (b) Using {E,g,o} as your K-set, use a standard Buckingham-II dimensionless analysis to find the exponents for a safe-radius coefficient of the form. Show all steps II₂ R = п, V BY c) Using the same K-set, use a standard Buckingham-II dimensionless analysis to find the exponents for a viscosity-scaling coefficient of the form. Show all steps VE g³ pr β γ = RE gp' Two early hybrid rocket tests showed that a malfunctioning rocket is indistinguishable from a bomb. Shell fragments from a zero-altitude explosion travel a distance R that can be considered a function of the following parameters: • the characteristic size L of the fragment (SI units of m), • the available combustion energy E within the chamber (SI units of J), • the rocket casing density p (SI units of kg/m3), • the local gravitational acceleration g (SI units of m/s2), • the atmospheric kinematic viscosity v (SI units of m2/s), and • the atmospheric sound speed a (SI units of m/s). (a) How many dimensionless groups are necessary to describe this problem, and why? (b) Using {E,g,o} as your K-set, use a standard Buckingham-II dimensionless analysis to find the exponents for a safe-radius coefficient of the form. Show all steps II₂ R = п, V BY c) Using the same K-set, use a standard Buckingham-II dimensionless analysis to find the exponents for a viscosity-scaling coefficient of the form. Show all steps VE g³ pr β γ = RE gp'

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Solution Parameters involved Dimensions DistanceR M 0 L 1 T 0 Characteristic LengthL ... View the full answer