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HomeworkSolutions_C1 - Problem#1 Consider a spherical...

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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 a function of: Particle diameter, d; the buoyant weight of the particle (weight of the particle minus weight of displaced fluid), W; fluid density, ρ ; and fluid viscosity, μ . Obtain the relationship for u using dimensional analysis. Suggestion: solving the set of linear equations in terms of the exponent of W. Answer: Note that mass, in physics, is the quantity of matter in a body regardless of its volume or of any forces acting on it. The term should not be confused with weight , which is the measure of the force of gravity (see gravitation ) acting on a body. Under ordinary conditions the mass of a body can be considered to be constant; its weight, however, is not constant, since the force of gravity varies from place to place. Therefore, the buoyant weight, W, is understood as the difference between the gravity and buoyant forces acting on the particle.
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