Radial Momentum

tt_95@yahoo.com

Radial Momentum is a property of fluid that explains lift

in the levitator and in other devices.

The Bernoulli Principle is a statement of conservation of energy.

Although it is correct, it does not explain lift

in the levitator and other devices.

Cool Toys

On this site, I present some cool toys

including a levitator, a paper cone

and some fancy squirt guns.

Levitator

Paper Cone

You can make a levitator

from a spool of thread and a card.

When you blow air down onto the card

the card sticks to the bottom of the spool!

Levitator

This is a diagram of how the air flows

down the tube and out across the card.

High School and College science books

try to explain how this curious device works

by using Bernoulli's Equation.

They say that Bernoulli's Equation says

that fast-moving air has low pressure.

From that, they say that since the air moves faster

over the top of the card than under the bottom of the card

the pressure above the card is lower

and the greater pressure below pushes the card up.

I claim that  Bernoulli's Equation

says nothing of the kind.

If it were true that fast air has lower pressure,

you could take a big old jar of air,

put an altimeter in the jar, screw on the top,

take the jar out for a fast ride in your car,

and see the pressure in the jar drop.

I claim that using Bernoulli's Equation

as an explanation for lift

constitutes out-and-out Bernoulli Abuse.

Stop Bernoulli Abuse

To prove my point, I run some experiments

Collapsing Cone Experiment

Non-Collapsing Tube Experiment

If fast air goes with low pressure,

both tubes would collapse

when you blow air through them.

Actually, only the cone shape collapses,

indicating the pressure drop

has something to do with the air

fanning out into a larger volume.

Levitator Table Setup

To get some precise measurements,

I build a levitator table, complete with instruments

to measure air pressure and air flow.

Cavitation Ring Experiment

I also predict the existence of a cavitation ring

and sure enough, I find one.

The Point of it All

This site presents the case

that levitation has to do with Radial Momentum,

not with fluid velocity.

The High School Physics Hoax

If you look in high school physics books

you may find a couple standard diagrams

Airplane Wing Cross Section

This diagram is part of a goofy theory

that since air flows faster over the top of the wing

and slower under the bottom of the wing.

the pressure on the top is lower

and therefore the wing rises.

You may recall seeing this diagram in high school.

You may also recall a feeling of confusion

about something being not quite right.

Large to Narrow Pipe Diagram

The same people who bring us the wing diagram

also bring us the large-to-narrow pipe diagram

to show how it all works.

They try to use this diagram to try to prove

that high velocity and low pressure go together.

Here's how their song goes:

I Claim this Math Represents Bernoulli Abuse.

First, the math is true only for self-containing systems.

Second, it is true only for constant density.

From #1: the only system for which you can use this math

is a self-containing hollow donut containing air.

From #2: the donut cannot have a fan in it to motivate the air to move.

In such a donut, there is nothing to move the air around the loop

so it comes to rest with zero velocity.

In this case, the math is, actually correct, since 0 = 0.

For cases involving air that actually moves around,

trying to use Bernoulli's Principle

to show that fast air goes with low pressure

is just plain goofy.

By the way,

the assumption about constant density is particularly goofy,

density change is the explanation for the levitator.

Radial Momentum Offers a Better Explanation

The Radial Momentum explanation is that

as the air fans out radially, from the center of the device

it expands into larger and larger volumes

and so it becomes less and less dense.

It is this lower density that explains the lower pressure.

To test this, I design the Tube and Cone Experiment .

The cone collapses and the tube does not collapse.

This indicates that air fanning out goes with pressure drop

and that fast air makes little difference.

The Cone Collapses

The Tube does not Collapse

To further test this out, I make a levitator table

that is basically a big plastic see-through version

of the spool of thread levitator

in which I can measure the air flow and pressure.

Fancy Levitator Table

The flow meter is on the left

and the pressure meter is on the right.

View from Underneath

The air flows through a 1/8" hole in the table.

I try my levitator table with various kinds of cards

Cards are easy to come by here in Nevada.

I find they all stick to the bottom of the table

when I blow air down the hole onto the cards.

Next I try my levitator table with smooth plastic disks.

The disks stick too.

Special Disks

Then I build some special disks - ones with channels.

Channel Disks

The point of the channels is to force the air

to flow in different ways.

Detail of Hourglass Channel Disk

I then try these disks with my levitator

to see what happens.

All the disks stick to the levitator

when I put the smooth side up.

When I put the channel sides up,

all except one sticks.

The one that does not stick

is the one with the parallel channel.

This is the only one that does not allow

radial expansion of the air.

So this is further evidence

that Radial Momentum, not air speed

is the explanation for lift.

The Professor and His Business Card

I show my results to a professor from a nearby college.

He specializes in fluid dynamics

and he says he thinks I'm crazy.

He says I am going up against 300 years of science

and that there is no way I'm right.

Furthermore, he shows me a pile of exam papers.

They are the final exams for his graduating college seniors.

The exam question has to do with, of all things, the levitator.

I point out the errors in the exams,

that are the same errors they have from his teaching them.

We are not really off on a good foot.

He tells me he has a way to prove he is right

about high velocity going with low pressure.

He suggests I build a table with a slit in it

rather than a hole in it.

The slit would broadcast air in a linear ribbon

that does not expand radially.

If the card sticks to a slit,

it would prove the velocity theory.

The Business Card Levitator Experiment

I build the experiment according to his suggestion.

The Slit Levitator

The air enters through the fitting at the right

and emerges out the slit that holds the card.

In operation, the card sits on the top plate

flat, between the "headboards."

To make it all the more dramatic,

I use one of the professors own business cards

as the levitation card.

I turn on the pump and run the experiment.

The card does not stick to the equipment.

This is further proof that radial expansion

and not air velocity is the correct explanation

for lift in the levitator.

I call the professor with the good news

that he and all his students have it wrong.

He is not happy with the news.

He does not want to discuss the matter further with me.

I assume he is still busy teaching bad science

to his seniors.

Fun with Water

I run further experiments with water.

The results are much more vivid.

Parallel Channel Water Nozzle

Hourglass Channel Water Nozzle

The Hourglass Works as a Levitator

Again, the parallel channel does not levitate.

The effect with water is stronger

since water is less compressible

so pulling it apart, even a little bit

generates a strong vacuum.

The Ring of Air

The Ring of Air

The basic radial Momentum idea is that the air

expands out radially, by momentum,

into larger and larger rings of air.

If the same mass of air occupies a larger volume

its density is less and the pressure goes down with density.

Note: the Ideal Gas Law states: pV = nRT.

(Pressure x Volume = amount x gas_constant * Temperature).

This law is by Emile Clapeyron, 1834

who combines Boyle's Law and Charle's Law.

Therefore pressure is proportional to density (n/V).

Computer Model

I build a computer model, using Radial Momentum as the organizing principle.

Computer Model Output

The model shows the pressure, velocity, density, mass and mass flux

running from the center of the disk (left) out to the edge (right).

The model shows the pressure drops right around center

in a region I call the active zone.

The pressure reaches a minimum in a ring around the central orifice.

This low pressure motivates the air to increase in velocity,

imparting additional radial momentum to the particles.

As these particles continue radiating outward from the center,

the fluid becomes less dense and the pressure falls.

As the particles flow past the minimum pressure ring,

they experience back-pressure and this tends to slow them further.

The velocity continues to fall until the Radial Momentum dissipates,

the pressure rises to slightly above ambient pressure

and the fluid gently drains at the edge of the disk.

The Cavitation Ring

According to the model, the lift effect occurs

in a small active region around the center of the disk.

I begin searching for evidence of this ring.

I take the equipment outside into the back yard

where I can use water to drive it.

Portable Levitator with Water as the Fluid

The jet from house travels about 30 feet.

If you hold your hand in front of it, it deforms your hand

and feels painful.

Close-Up of the Portable Levitator

The water emerges through a small hole in the center of the disk.

Bringing the Disk up to the Levitator

The stream of water hits the disk and sprays everywhere.

The stream is still pushing the disk away.

Note: experimenters sometimes have to subject themselves

to enormous hardships in the pursuit of scientific knowledge.

Levitation

When the disk comes flush with the levitator, the levitator "captures" it

The disks stick together with several pounds of force.

Consistent with the Radial Momentum model,

the water gently emerges from around the edge of the disk.

Levitation, another View

The author uses his left hand to keep the disk from sliding to the side.

He is applying little or no upward pressure on the disk.

The stream of water from the hose is levitating the disk.

It Works Under Water

I test the effect under water, at the suggestion of a colleague.

The effect works under water.

Without the levitation effect holding the disk to the levitator,

the water jet from the hose would shoot back out of the dish.

Looking for the Ring

Underside of the Levitator (upper left).  The disk (lower right) has a handle on it.

I first run the test at low pressure, by crimping the hose.

I notice a faint white ring around the central hole.

This is a ring of tiny air bubbles,

emerging from the water

as the low pressure sucks them out.

Turning up the Flow

I let the hose go a little bit, increasing the flow.

The cavitation ring becomes bigger and whiter.

Even More Flow

The ring gets bigger and whiter.

Maximum Flow

I let the hose go, full on.

The ring gets even bigger and whiter.

Other Rings

Water on the Back of a Dish

You can see a very thin layer of water

in the "active region" in the center of the dish

and a "hydraulic jump" a couple inches from the center.

This is similar to the pressure profile of the levitator.

Jet Aircraft with Trailing Ring

My guess is that the nose of the craft (and the cockpit)

divert the air into an expanding ring pattern

so the air expands radially around the nose-to-tail axis.

This results in a decrease of pressure and temperature

in the active region - and the humidity in the air

condenses momentarily to produce a visible cloud.

Other Evidence

Flow Versus Pressure for a 3.9 oz. Disk Using Air

I take some measurements on the levitator table

to determine the flow versus pressure chart.

For low head pressure (from the pump)

the flow is about 2.5 standard cubic feet per minute.

As the pressure rises, the flow decreases !

This is due to the levitation effect

bringing the disk closer to the levitator

and restricting the flow.

Conclusion

Levitator lift is a function of Radial Momentum.

Fast or Slow air has nothing to do with it.

The Bernoulli equation is an energy balance equation.

It does not apply to the levitator.

Word of Caution

Stop Bernoulli Abuse.

Daniel Bernoulli (1700-1782)

"It would be better for the true physics

if there were no mathematicians on earth."

-- Daniel Bernoulli

The End (for now).