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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 Fall '08
 Peters
 Buoyancy, Fundamental physics concepts, Incompressible Fluids, buoyant weight

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