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 uof 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 ucan 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). abcduCD W Obtain the relationship for uusing 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 band care correlated. Problem #2: The power required to rotate a drilling string is a function of string diameter D, number of
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