Solution_HW1 - Solutions for homework set #1: Problem #1:...

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Solutions for homework set #1: 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). ab c d uC D W ρμ = 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. Answer: If c d D W = Equating dimensions: Solving in terms of c: a = -1 b = 1+c d = -(1+2c) 11 2 1 2 2 cc c c c D W WW C D DW W ρ μμ μρ μ
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Solution_HW1 - Solutions for homework set #1: Problem #1:...

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