HW_1 - Homework Set #1: Due date: 09/07/07 by 11:00 am...

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Homework Set #1: Due date: 09/07/07 by 11:00 am 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). abcd uC DW ρµ = Obtain the relationship for u using dimensional analysis in which the set of linear equations is solved in terms of the exponent
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