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Calculate Air Speed

10/17/2015 5:49 PM

Imagine a car which is 14 feet long. I have installed an airtight metal pipe along the length of the car. The pipe has a diameter of 12 inches at the front. After 1 foot, i.e at 13 feet, the pipe's diameter is reduced to 2 inches. The rest of the pipe till the end (from 13 feet till end) is now 2 inches in diameter.

Imagine the car is traveling on the highway at a constant speed of 50 miles an hour. I want to calculate the velocity of the air coming out of the rear end of the pipe. There are no impediments inside the pipe. It is a straight pipe. Air is flowing in at the front opening which is 12 inches in diameter and it coming out from the other end where the diameter is 2 inches.

I want to calculate the relationship between the front diameter and the rear diameter and the speed at which the air will be coming out from the ear end. Suppose the front diameter is now 14 inches and the rear diameter is 4 inches, keeping the length of the pipe to be identical, i.e 14 feet.

Because of the reduced diameter, the air coming out will be significantly higher force than the air being sucked into from the front end when the car is moving at a constant speed of 50 miles an hour. There has also to be relationship between the speed at which the car is moving. At lower than 50 miles/hour, say 30 miles/hour, the air coming out of the pipe at the rear end will be at a lower speed as compared at 50 Miles/hour. Similarly, at higher speed, say 90 miles/hour, the air coming out of the pipe at the rear end will be at a much higher speed as compared at 50 Miles/hour. What is that relationship?

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#1

Re: Calculate air speed

10/17/2015 6:04 PM

reading and understanding rules seem to escape you

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#2

Re: Calculate air speed

10/17/2015 7:02 PM

Wow. You seem to have little to no understanding of fluid, let alone compressible fluid mechanics. You don't seem to even know how to properly specify a problem. An air tight metal pipe has no holes in it. Holes allow air to enter or leave. You also have not established any inertial frame of reference.

It sounds like you are trying to make a lossy version of a pitot system used in aircraft to measure air speed.

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#3

Re: Calculate air speed

10/17/2015 7:45 PM

There would be so much turbulence, pressure and friction, that there would be probably no increase in wind speed...

This is the result of flawed logic and an absence of knowledge about fluid dynamics...

http://cleantechnica.com/2014/07/08/invelox-ducted-turbine-latest-long-line-failures/

https://en.wikipedia.org/wiki/Fluid_dynamics

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#4

Re: Calculate air speed

10/17/2015 9:13 PM

Its just like a jet propulsion turbine, cut off from power on air.

Try Fibonnaci proportions

You need to study, mass rate, 1st law of thermodynamics and second law as well.

It's like parachute with hole in the end of the dome, as it goes down, there is no way its gonna speed up, not unless you have to make the hole bigger that it could approach harmony with gravity.

It's fun learning.

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#5

Re: Calculate air speed

10/18/2015 2:25 AM

Schrodinger's cat will die.

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#6

Re: Calculate air speed

10/18/2015 7:12 AM

The volume of air flowing in is equal to the volume of air flowing out, or velocity_in x area_in = velocity_out x area_out. Having said that, realize that the velocity in won't be 50 mph, and here's why. It takes force to speed up the air in the funnel. This force manifests itself as back pressure which decreases the flow into the front and increases the drag.

In the end, I suspect the air won't be flowing out much faster than the outside air.

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#7
In reply to #6

Re: Calculate air speed

10/18/2015 8:04 AM

Rixter, You are one who has given a sensible answer without insulting. Let us continue the discussion. What I am imagining is a funnel type situation, where the outside diameter is say 12 inches and the other end is 2 inches in diameter. The intake is 12 inches, the motion of the car at 50 Miles/hour is providing the Force. The other end is 2 inches in diameter, the length of the pipe is 14 feet total. From the rim of the funnel to the base where the aperture is reduced to 2 inches is 1 feet. The rest of the pipe is 13 feet long.

Compare this with a 12 inch pipe that has water flowing at a constant pressure. the pipe is now reduced to 2 inches in diameter, like a funnel. The water pressure at the end of the funnel will be many times more in comparison to the water flowing when the diameter is 12 inches. I am trying to find how many times it is and when we are using air and not water. Hope you will answer soon.

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#8
In reply to #7

Re: Calculate air speed

10/18/2015 8:17 AM

you're a slow learner. FIRST once you actually READ the forum rules! you just might notice email addresses are specifically mentioned as a no no.

it might shock you yo learn BOTH water and air are fluids, you seem to think they differ

and Rixter isn't a member, he's the janitor. he only has a key so he can get om here to dump the trash.

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#10
In reply to #7

Re: Calculate air speed

10/18/2015 11:24 AM

KA10900@gmail.com,

You seem to think that all responders besides Rixter insulted you.

I think that you insulted the intelligence of all members here by asking a multiple part, ridiculous, unintelligible question and expecting a serious response.

Where did you seek answers before coming here?

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#16
In reply to #10

Re: Calculate air speed

10/18/2015 11:38 PM

Why do you almost always discourage people from learning?

I agree that his sentence structure is terrible, and he clearly has much to learn, but at least he is trying to learn something. That places him a BIG step ahead of many others in my book!

Yes, he is asking a multiple-part question, but all of those parts relate to fluids flowing through tubing of varying diameter, and he did clarify that its a funnel, not a bucket at the entrance.

I guess I was fortunate never to have a professor with your condescending attitude!

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#17
In reply to #16

Re: Calculate air speed

10/19/2015 12:19 AM

OK, I missed the funnel part.

I also missed any prologue that would explain his motivation for the question.

I admit that I'm intolerant and at times blunt or even rude.

KA10900@gmail.com, dkwarner is right. I should have stayed out of the discussion.

My apologies to you.

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#18
In reply to #10

Re: Calculate air speed

10/19/2015 3:16 AM

I have to agree with your comments here.

The OP has not "earned" an answer, any answer......probably a homework question?

I'm off, byeeee!

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#11
In reply to #7

Re: Calculate air speed

10/18/2015 11:50 AM

This is computation fluid mechanics simulation you are talking about.

I guess this is homework, or may be you just skipped the class during the discussion of this.

This is a simple thing to start, read. FDSimulation

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#12
In reply to #7

Re: Calculate air speed

10/18/2015 5:44 PM

Neglecting friction (viscosity) the pressure on the output will be the same as the pressure on the input. The volume entering will be the same as the volume exiting. Pressure x volume = Energy. (lb/sqft x cu ft = ft lb. ) So, neglecting losses, the energy coming in equals the energy going out.

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#13
In reply to #12

Re: Calculate air speed

10/18/2015 5:59 PM

So, we've got a 12" dia cylinder with a flat bottom with a 2 " dia hole in it that feeds a 13' long 2" diameter pipe.

"After 1 foot, i.e at 13 feet, the pipe's diameter is reduced to 2 inches. The rest of the pipe till the end (from 13 feet till end) is now 2 inches in diameter."

My interpretation of this nonsensical sentence looks like a straight sided bucket with a 2" hole in the bottom.

Turbulence inside the bucket will negate most of the flow into the 13' of straight pipe.

I don't see any way to un-muddle this mess.

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#20
In reply to #13

Re: Calculate air speed

10/19/2015 8:06 AM

Here's a stab at it. I don't know if it's right...

Area of 12 dia circle: A = .785 sqft. = 113 sq in

Speed 50 mph: V = 73.33 ft/sec.

Volume of air hitting funnel per second: delV = .785 x 73.33 = 57.56 cu ft

mass of air per cu ft: D = .002375 slug/cuft

mass of air hitting funnel per second: D x delV = .002375 slug/cuft x 57.56 cuft/sec = .137 slugs/sec

Force = m delta v = .137 slugs/sec x 73.33 ft/sec = 10.02 slugs ft/sec2 = 10.02 lbs

Over pressure in funnel = 10.02 lbs / 113 sq in = .089 psi

However much air an extra .089 psi will push through a 2 inch hole...

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#23
In reply to #12

Re: Calculate air speed

10/19/2015 12:00 PM

"The volume entering will be the same as the volume exiting." That would be true for water (non-compressible), but not for air (compressible).

The velocity of the air in the small tube must be greater than that in the large tube, and Bernoulli tells me that the higher velocity air should have a lower pressure, and thus a larger volume.

The mass entering will be the same as the mass exiting.

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#31
In reply to #23

Re: Calculate air speed

10/20/2015 7:42 AM

Good point, there is a small correction for change in density with pressure.

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#9

Re: Calculate air speed

10/18/2015 8:24 AM

The air exiting the hole in the parachute is at such high velocity that it actually pushes the parachute down, causing the rider to fall even faster. Or, at least that seems to be the OP's desired scenario. Of course, something is wrong with that picture.

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#14
In reply to #9

Re: Calculate air speed

10/18/2015 7:31 PM

I think in the case of the parachute, you could take the weight of the payload and divide by the area of the base of the parachute. That would give you the over pressure required to support the payload. (Very slightly above ambient pressure). That much over pressure would push some air out the hole at the top.

(Not enough thrust there to drive him into the ground!)

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#15
In reply to #14

Re: Calculate air speed

10/18/2015 9:18 PM

I was kidding, but my emoticon menu doesn't work.

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#19

Re: Calculate Air Speed

10/19/2015 6:59 AM

A picture paints a 1,000 words.

I appreciate you might be happy to write a 1,000 words, but regretfully I have not got time to read a 1,000 words - time and time again - to make sense of what you are describing - especially when a picture would do it in a few seconds.

Perhaps it's my age. Good luck with your question.

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#21

Re: Calculate Air Speed

10/19/2015 9:38 AM

Here is a cad model of it.

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#24
In reply to #21

Re: Calculate Air Speed

10/19/2015 12:18 PM

After reading post #7, I see it as this:

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#25
In reply to #24

Re: Calculate Air Speed

10/19/2015 12:38 PM

I didn't read #7. I was going off of the original posting!

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#26
In reply to #24

Re: Calculate Air Speed

10/19/2015 12:54 PM

Yes, this is correct.

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#27
In reply to #26

Re: Calculate Air Speed

10/19/2015 1:56 PM

All the math you need is HERE.

-A-

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#22

Re: Calculate Air Speed

10/19/2015 10:45 AM

KA10900,

We actually don't need the car. We just need to know if the incoming air is laminar or turbulent ( I think we can assume laminar flow for the sake of a thought experiment). Also, we need to know the shape of the transition between the two diameters (Sharp edge, well rounded, tapered, etc.). It really does matter a great deal. Lastly, we need to know the internal roughness of the pipe.

All these things are going to be necessary to calculate the frictional losses in the pipe. The sum of all the frictional losses are going to give you the differential in pressure between the two ends of the pipe. For a given amount of fluid (air) passing through a fixed area (the end of the pipe), we can use the pressure to calculate velocity.

This type of problem is covered repeatably in a "Fluid Mechanics" class. Non-engineer types may have difficulty understanding how to model a simple problem like this.

Kudos to you for trying.

-A-

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#29
In reply to #22

Re: Calculate Air Speed

10/19/2015 3:42 PM

Hi -A-,The incoming air is Laminar. The shape of the entire thing is very smooth. No internal roughness. Imagine this piece made out of a single PVC pipe. One end is a funnel having 12 inch diameter and the other end of the funnel is 2 inch diameter. This is not for any homework or any project from a class. I would like to get a way to calculate the force or power of the air coming out of the tail end, when the car is moving at 30 mph, 50 mph and 90 mph. I understand that the volume of air coming out will be equal to volume of air coming in. I would also like to calculate the relationship between the increase in the force at which the air comes out of the smaller end when the diameter of the funnel increase or decreases. My understanding is, larger the funnel diameter and smaller the funnel tip (other end), the greater will be the force with which the air will come out. If you guys think I am stupid, so be it. I take it as a complement. Please answer my question.

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#30
In reply to #29

Re: Calculate Air Speed

10/19/2015 5:46 PM

First: I"m no expert on fluid flow! ...but I'm pretty sure you can't have laminar flow when there are sharp corners. Here I've moved the funnel back 4", added a 4" long piece of 12" tubing on the front, and then put a 10" radius on the transitions between cylinders and cones. I'm pretty sure this will be more likely to approximate laminar flow.

Now, I suspect that you are looking at this as a means of generating energy. As soon as you put a turbine in that tube (or in the air stream just outside the tube) to try to generate electricity or otherwise extract energy, all the formulas change, because the turbine (or anything else blocking the flow) will exert back pressure on the fluid, and slow it down significantly. The energy thus generated would be a tiny fraction of the energy required to drag the apparatus through the air.

In other words, the net effect of the assembly would be to significantly increase the fuel consumption (reduce the mpg) of the car.

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#32
In reply to #30

Re: Calculate Air Speed

10/21/2015 12:52 AM

I think its a funnel use for wine maybe. Or may be a trumphet? I dont know.

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#33
In reply to #32

Re: Calculate Air Speed

10/21/2015 1:04 AM

Wine? ...on top of a car traveling up to 90 mph?

Not MY wine!

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#34
In reply to #33

Re: Calculate Air Speed

10/21/2015 3:50 AM

It did look like the thing, i dont know.

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#28

Re: Calculate Air Speed

10/19/2015 2:18 PM

Does the air have velocity? If the air has no velocity of it's own as this car speeds by. Channeling it down this pipe to leave it behind in the same space. The only velocity will be it the direction of the cars movement. As turbulence and friction applied going down the pipe would drag it along.

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#35

Re: Calculate Air Speed

10/23/2015 7:03 PM

I almost hate to get into this foray; but, here is the simple answer to what appears to be the basis of the original question. Ignoring the fine points of air flow profiles entering the orifice at the cone/ tube interface and the flowing friction through the tube, the following sums up this situation.

As the incoming air strikes the cone the dynamic velocity pressure is converted to static pressure and when that static pressure energy is then converted flowing pressure energy and a higher velocity through the 2" tube will create a high velocity thrust on the the tube assembly; BUT, here is the catch, the total added thrust of force of that air steam will be completely offset by the incoming lower velocity air striking the larger diameter cone face, so the net force on the cone/tube assembly is fully balanced by:

slow velocity x large area = high velocity x small area

Obviously that is not the exact equations but the final result is still the same i.e. no added thrust on the cone or car.

In fact, the end result, will be to add additional drag to the car as the air striking the cone results in more frontal area drag as the incoming air velocity energy is converted into static pressure energy as it strikes the cone face.

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#36
In reply to #35

Re: Calculate Air Speed

10/24/2015 12:49 AM

I am replying to my own previous post to correct an error that I realize I made in describing the process of conversions of the flow. In my original post I inadvertently selected a fixed cone/tube with an approaching air flow which is incorrect for the automobile with a cone tube assembly attached. The final statement about force balancing is correct but the static to dynamic and energy conversion series is incorrect.

First, it is necessary to understand that (barring any external energy additions) in any gas the total pressure energy = static pressure energy + dynamic pressure energy to put it the simplest terms; and, as one increases the other decreases accordingly so that the total value never changes.

For the auto and cone/tube in motion through still air. The process starts with static air which as the cone/tube moves forward is progressively converted into dynamic flow as it is driven into the 14" cone where it progressively accelerates as the air is pushed down the cone to 2" the tube entrance where it reaches it maximum velocity inside the 2" tube. As a result, there is a high velocity air flow and thrust exiting the tube that then progressively slows as it regresses back the same static pressure it possessed before being impacted by the cone /tube unit.

From this point forward the original post statements (with minor revisions) regarding the force balances still remain valid. To Quote:

"BUT, here is the catch, the total added thrust of force of that air steam will be completely offset by the incoming lower velocity air striking the larger diameter cone face, so the net force on the cone/tube assembly is fully balanced by:

Edited: Static pressure x large area resistance = high velocity x small area thrust force

Obviously that is not the exact equation but the final result is still the same i.e. no added thrust on the cone or car.

Edited: In fact, the end result, will be to add additional drag to the car as the air striking the cone results in more frontal area drag due to energy losses as the static air is accelerated through the cone and flowing friction losses as the air flows through the tube."

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#37
In reply to #36

Re: Calculate Air Speed

10/24/2015 1:23 PM

Hi JAlberts,

I am looking for a mechanism by which I can measure the velocity of the air coming out of the tail end of the funnel when the car is moving at 30mph, 50mph, 75mph, or 90mph. For all practical purposes just assume that the assembly, i.e the funnel is some how attached to the front of the car and goes all the tail goes all the way to the back of the car. For the moment, please forget about the beauty aspect. Once again, this is not a homework question or a class project for a grade.

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#38
In reply to #37

Re: Calculate Air Speed

10/24/2015 5:14 PM
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#39
In reply to #37

Re: Calculate Air Speed

10/25/2015 7:19 PM

KA10900

Do you want to calculate it; or measure it?

Just as a note with regard to the length of the tube, the longer the tube the more flow friction, pressure drop and lower velocity at the end of the tube. The most efficient arrangement will be the shortest tube. The maximum velocity in the tube will be just beyond the entrance to the tube because that point acts as a 2" orifice that establishes the maximum velocity in the tube before any friction losses as the air flows through the length of the tube.

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