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HW_1 - Homework Set#1 Due date by 12:00 PM Problem#1...

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Homework Set #1: Due date: 09/09/10 by 12:00 PM Problem #1: Consider a spherical particle falling freely in a large fluid body. It is found experimentally that the terminal settling velocity u of the particle is dependent on: (1) particle diameter D; (2) the buoyant weight of the particle W (the difference between the gravity and buoyant forces acting on the particle); (3) fluid density ρ , and (4) fluid viscosity μ . It is assumed that the velocity u can be mathematically expressed as products of powers of the above variables (i.e. similar to the example of dimensional analysis given in the previous lectures). a b c d u CD W   Obtain the relationship for u using dimensional analysis in which the set of linear equations is solved in terms of the exponent c . Show that the respective dimensionless groups obtained by solving the set of linear equations in terms of the exponent b and c are correlated. Problem #2: The power required to rotate a drilling string is a function of string diameter D, number of
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