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Name: Kim
Status: Student
Grade: 9-12
Location: NY
Country: United States
Date: March 2008


Question:
I have learned in Earth Science that larger, more dense, spherical particles settle first in still water. However, I was wondering why this happens? How do density, size, and shape of an object affect its settling rate?



Replies:
Kim,

It is a matter of competing forces. The force that is pulling the particle down is gravity, f = m*a. As the particle gets larger and denser, m (mass) increases. The opposing force is the friction of the water, which also increases with the size of the particle and its shape (with more friction as its surface area increases) .

So for example, with two particles of the same mass and density, the one with the larger surface area (thus more friction) will settle slower. Two particles of the same size and shape, but different density, the one with the higher density (more mass) will settle faster.

There are various other permutations, although it is harder to know without calculations or experimentation which will settle faster if you vary more than one characteristic at a time.

Don Yee


Kim,

You may have heard that the two objects fall at the same rate, that the speed at which they fall is only dependent on the gravity (which is the same if they are at the same distance from the center of the Earth) and this may have led you to think that it will be true also for settling objects in fluids. This is no longer true because a fluid like water may affect falling (or settling) rates unlike a fluid like air. Water, being more dense then air, can have a buoyant effect on objects. For example a piece of wood may float in water, but a similarly shaped piece of metal will sink. On the other hand, a similar mass of metal that is shaped like a hollow sphere, may float on water because the amount of displaced water has a mass that could be greater than the metal object. So, unlike air which has a small buoyant effect (the mass of air displaced by an object is small relative to the mass of the object), water, being denser than air, will have a much bigger displaced mass, and have a stronger buoyant effect.

Thus, objects will fall at different rates in a denser fluid like water because the buoyant effect on the objects will be different.

Greg (Roberto Gregorius)


Kim,

Spherical particles may settle more rapidly because their smaller surface area (than say an irregularly shaped particle) causes less frictional drag force. Thus they can settle fastest, assuming that all other factors (size and mass) other than shape and irregularity of particles are held the same.

More dense (larger mass per unit volume) particles are heavier and thus for the same size particle (heavy versus light) gravity will act more on the denser particle, making it settle faster.

Larger particles, having more mass than smaller particles (assuming that their density is the same) will settle faster because gravity has greater affect on them.

Of course, we are talking about "larger" particles here with greater density than water, as very small particles (especially if they have the same density as water) can become suspended in a fluid. Particles with less density than the fluid should float.

Kim's question could make it a bit confusing, as she said "larger, denser, spherical".

The answer could be just "yes", but I wanted to explain further.

Frictional forces exerted by the medium through which the particle is falling cause the fall rate to slow and eventually reach the terminal velocity. The fall rate therefore depends on mass, size, and shape of the object, as well as the density of the medium. I did not want to confuse Kim with terminal velocity considerations.

If two particles have the same diameter, the one with greater density (defined as mass per unit volume), and thus greatest mass, will fall fastest because gravity will act more upon it.

If two particles have the same density, but different diameters (and thus different mass), it may seem as though the one with more mass may fall faster, but that one also experiences greater frictional forces imposed on it by the medium. Equations would have to be used to determine which would fall fastest.

If two particles had the same mass and density, the one that is more streamlined (spherical) would fall faster than one that is irregularly shaped, because frictional forces in the medium would act more upon the irregularly shaped particle, thereby slowing it's fall more.

In a way, Galileo's experiment was flawed. There was not sufficient distance during the fall for weak air frictional forces to have much of an effect on the two falling objects. If they had been differently shaped, like a feather and something round of the same mass as the feather, or if the experiment had been performed from the top of the Empire State Building or Sears Tower, the results would have been different. The fall rate for two objects of the same mass but different shapes is only the same in a vacuum, where frictional forces can not act (which is not a real life situation).

David R. Cook
Meteorologist
Climate Research Section
Environmental Science Division
Argonne National Laboratory


Oops, I somehow sent it before I finished. onward...

Again, you are right that the buoyancy force is equal in magnitude to the weight of fluid displaced. I have a hard time getting that across to my students in one mouthful, because in that tiny little phrase is contained the concepts of gravity, density, and displacement. So I just stated that buoyancy is proportional to volume, which is true as long as the object is completely submerged.

So I propose this as another iteration of the paragraph with your two comments:

"The settling rate is the speed at which the viscous drag acting on the settling particle exactly opposes the downward force on the particle. That downward force is the interaction between the downward force of gravity on the particle and the upward buoyancy force. (I have grouped the forces in this way because the force of gravity and the force of buoyancy are the same at any speed the particle might move. The force of viscous drag, however, changes with speed.)

The larger the object is, and the denser it is, the greater the gravitational force acting downward on it. The force of buoyancy on the object is how much the water pushes it upward. The strength of this buoyancy force is proportional to the volume of the object. (It is actually equal to the weight of the water displaced by the particle, which is equal to the weight of a volume of water equal to the volume of the particle.) If the particle is more dense than water, its gravitational force exceeds its buoyancy force and the net force on the particle is downward. If the particle is less dense than water, its buoyancy force is stronger than the gravitational force and the net force on the particle is upward."

Richard Barrans, Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming



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