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Re: centrifuge exercises

I DID FORMULATE THE PROBLEM (SEE BELOW) BUT
I CAN NOT SOLVE PART B WITHOUT IGNORING WATER
RESISTANCE. IGNORING WATER RESISTANCE (STOKE)
IS RIDICULOUS; IT LEADS TO A CONCLUSION THAT
THE SEDIMENTATION TIME DOES NOT DEPEND ON
SIZES OF PARTICLES. THE BASIS FUNCTION OF THE
CENTRIFUGE IS NOT ACCOUNTED FOR.

CAN IT BE ASSUMED THAT STOCKES FORMULA IS
VALID UP TO VELOCITIES OF SEVERAL M/S IN
WATER? PROBABLY NOT. I NEED HELP AGAIN.

IF THERE WERE NO WATER RESISTANCE THEN A
PARTICLE OF ANY SIZE, AT REST WHEN R=9 CM,
WOULD HIT THE BOTTOM OF THE TUBE AT
V=27.3 M/S (WHEN W=100 RPS) AFTER ONLY
0.00073 S. THIS IS A SMALL FRACTION OF ONE
ROTATION.

John D wrote:

Earlier you had declined repeated suggestions to invoke
Stokes law of viscosity because it hadn't been covered
yet. Since you now seem to have changed your mind
about that, we can begin to address the bio-lab centrifuge.

I did use Stoke in part (a) but can I also use it in part (b).

************************************
Problem for Chapter 9 (Serway and Faughn).
************************************
Assume that the inner cavity of a glass tube is cylindrical.
A muddy water is poured into the cavity to the height of
1 cm. To simplify assume that all mud particles are
aluminum spheres whose radii are 0.001 mm

a) The tube is positioned vertically at rest. How long will
it take for all particles to settle? Assume the water
temperature is 20 degrees C? (THE ANSWER IS 2700 s)

b) An identical tube with the same amount of muddy water
is placed into a centrifuge, as illustrated in Figure 9.46.
The position is horizontal and the bottom of the container
is 10 cm away from the axis of rotation. (Imagine that a
cover is used to make sure the liquid is confined to the
bottom of the tube.) How long will it take for all particles
to settle if the tube is making 100 rotations per second?
The problem is to be solved by ignoring gravity.

Hint: (Use the average radial acceleration between r=9 cm
and r=10 cm.)

c) Why can the effect of gravity be neglected at w=100 rps?

Answers:
2700 seconds for (a) and .... seconds for (b). Earth gravity has
a negligible effect r*w^2 >> 9.8