(a) The Stokes number, St, used in particle-dynamics studies is a dimensionless combination of five variables: acceleration of gravity g, viscosity µ, density p, particle velocity U, and particle diameter D. If St is propotional to u and inversely propotional to g, find its dimensionless form.

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QUESTION 4 |
(a) The Stokes number, S1, used in particle-dynamics studies is a dimensionless combination
of five variables: acceleration of gravity g, viscosity µ, density p, particle velocity U, and
particle diameter D. If St is propotional to u and inversely propotional to g, find its
dimensionless form.
(b) When tested in water at 20°C flowing at 2 m s'', an 8 cm diameter sphere has a measured
drag force of 5 N. Determine the velocity and drag force on 1.5 m diameter weather balloon
moored in sea-level standard air under dynamically similar conditions?
(c) The power, W, generated by a certain windmill design depends upon its diameter, D, the
air density, p, the wind velocity, V, the rotation speed, 2, and the number of blades n. By
using velocity V, diameter D and density p as the repeating variables, prove the
dimensionless relationship is given by
W
Ω
pD?y³
Dyn
Transcribed Image Text:QUESTION 4 | (a) The Stokes number, S1, used in particle-dynamics studies is a dimensionless combination of five variables: acceleration of gravity g, viscosity µ, density p, particle velocity U, and particle diameter D. If St is propotional to u and inversely propotional to g, find its dimensionless form. (b) When tested in water at 20°C flowing at 2 m s'', an 8 cm diameter sphere has a measured drag force of 5 N. Determine the velocity and drag force on 1.5 m diameter weather balloon moored in sea-level standard air under dynamically similar conditions? (c) The power, W, generated by a certain windmill design depends upon its diameter, D, the air density, p, the wind velocity, V, the rotation speed, 2, and the number of blades n. By using velocity V, diameter D and density p as the repeating variables, prove the dimensionless relationship is given by W Ω pD?y³ Dyn
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