This preview shows pages 1–2. Sign up to view the full content.
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.
abcd
uC
dW
ρμ
=
If
()
(
)
( )
b
cd
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas at Austin.
 Fall '08
 Peters

Click to edit the document details