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 Abhi June 30, 2002 10:58

Terrible Mistake In Fluid Dynamics History

Time Vs Energy

Abstract: This article deals with instantaneous (superluminal) transfer of information.

Introduction: When we OPEN the valve of garden hose connected to water reservoir at greater height, with hose full of water, water begins to flow out due to gravity. Established knowledge of fluid dynamics states that this information travels across full length of hose pipe back to water level in reservoir through pressure waves with appropriate acoustic velocity in hose pipe. When these pressure waves reach to water level in reservoir, only after that water level comes down. This is not true. If it is true, then we can use this time interval of information transfer to create "free" energy.

Fluid Flow Analysis Under Gravitational Field: Consider a reservoir of full of fluid. Let height of fluid level in this reservoir from earth surface be h. Inlet A of horizontal pipe of length L is attached to bottom of reservoir. At outlet B, there is vertical empty pipe of height H and volume U. Let H = h + x where H > h. So height of vertical pipe i.e. "H" is greater than height of fluid level in reservoir i.e. "h". Let a be cross sectional area of horizontal pipe of length L and b that of vertical pipe of height H. Let b = or < a. So cross sectional area "b"of vertical pipe is equal to or less than cross sectional area "a" of horizontal pipe. Let c be velocity of propagation of pressure waves in pipe. Let t be time taken for these pressure waves to reach to inlet A from outlet B. Hence t = L/c. Let U be volume and v be average velocity of fluid entering in horizontal pipe during time interval t.

Hence t = (L / c) i.e. L = ct ...................Equn. (1) U = avt = bH where b = or < a ...............Equn. (2) H = h + x where H > h ..........................Equn. (3)

At time T = 0, fluid is flowing in system of reservoir and entire horizontal pipe of length L. At time T = 0, outlet B of horizontal pipe is connected to vertical empty pipe of height H so that flow of fluid in horizontal pipe is directed in upward direction in vertical pipe.

This information regarding change in situation i.e. pressure change at outlet B will travel through pressure waves with acoustic velocity c and reaches to inlet A after time interval t. But fluid flowing in inlet A has no information about situation change at outlet B during this time interval t, hence U volume of fluid will flow in inlet A during this time interval t. After time t, system of horizontal pipe and vertical pipe is isolated. At time T = 0, entire horizontal pipe of length L was full of flowing water. After time T = t, U volume of fluid has entered in closed pipe system of horizontal pipe of length L and vertical pipe of height H. Hence only way to accommodate this U volume of fluid is vertical pipe of height H. Hence there will U volume of fluid in vertical pipe of height H after time t.

Let d be density of this fluid. Hence mass of fluid of volume U, m = Ud.

(1) At time T = 0, when this fluid of mass m was in reservoir at height h, its potential energy, PE = mgh. (2) At time T = t, when this fluid of mass m is in vertical pipe of height H, its potential energy, PE = mgH.

But H = h + x and H > h hence mgH = mg(h + x) = mgh + mgx i.e. mgH > mgh

Only force acting on fluid in system is Gravity. There is no other force present in system. Then where from this extra PE equal to "mgx" came?

Query: (1) It is true that when we close the valve of pipe to stop flow of fluid, this information travels back to reservoir through pressure waves with appropriate acoustic velocity. This has been experimentally verified perhaps hundreds of times and all the scientific data regarding velocity and way of propagation of sound waves, hammer effect is correct.

But during flow of history, somewhere mistake is done. It is "assumed" that what happens to flowing fluid after CLOSURE of valve must happen to steady fluid(having only PE) when we OPEN the valve and then to uninterrupted flow of fluid. And this "assumption" is being treated as "truth" and NEVER at any time in history has been experimentally verified.

If reader believe that it is experimentally verified then when, where, who, how?

(2) Consider the situation when fluid is not flowing in the system given above. Fluid is just steady under gravitational field having potential energy. Pressure of fluid all over horizontal pipe attached to bottom of reservoir is same. That means pressure of fluid near inlet A is same as near outlet B. Now the person near outlet B opens the valve at t = 0 and fluid begins to flow out with velocity v.

But consider that the person at inlet A closes valve at t = 0 i.e. the moment the person at outlet B opens the valve. So the contact of fluid in reservoir has been cut off with fluid in horizontal pipe. Remeber that fluid is NOT flowing through inlet A because information regarding opening of valve at oulet B is not reached to inlet through pressure waves. As the closure of valve at inlet A will have no effect on pressure of fluid on both sides of valve at inlet A, so no information regarding pressure change will travel to outlet B. And we find no way through which this information regarding closure of valve at inlet A will be communicated to outlet B.

Question arise, the contact of fluid in reservoir has been cut off at t = 0, still, will the fluid flow out of outlet B with velocity v ? (Remember that outlet B at t = 0 don't have information regarding closure of valve at inlet A at the same moment i.e t = 0)

(3)Consider isolated vertical pipe full of water. water begins to flow out when valve at lower end is opened. Established knowledge of fluid dynamics state that this information travels upwards with appropriate acoustic velocity(about 1482 m/s) in pipe through pressure waves i.e. longitudinal waves of compression and rarefaction. water level comes down only when pressure waves reaches to upper water level.

Consider that temperature of water is decreased so that ice rod is formed in this vertical pipe. Let A be lower end of this ice rod and B be upper end. Valve is removed so that ice rod comes down freely due to gravity. Explanation of superluminal transmission of information states that this information regarding motion of lower end A travels through rod to upper end B through electromagnetic waves.

When temperature of water(or any fluid) in pipe is decreased, then PRECISELY at what water temperature this mode of transfer of information changes from pressure waves(longitudinal waves, speed 1482 m/s) to electromagnetic waves (transverse waves, speed 299792428 m/s)?

(4) Cause of pressure is gravity and when we open valve water just falls. And if we jump from tall building, I think that we will feel weightless. we will not be able to exert pressure on our shoes. How can water molecules exert pressure on each other while falling in weightless condition? If there is no pressure, how can it change? If there is no pressure change, how can it travel back with sound velocity?

(5) Consider that there are two horizontal pipes attached to bottom of reservoir at same depth. Length of first horizontal pipe is just 3 centimeter and length of second horizontal pipe is 3 million Km. Closed valves are attached to other ends of both pipes. Reservoir and both horizontal pipes are full of fluid. Now as pressure depends upon depth, pressure of fluid in both pipes must be same. If we open valve of both pipe, fluid will begin to flow. But velocity of fluid flowing out from 3 centimeter long horizintal pipe will be greater than velocity of fluid flowing out from 3 million Km long pipe.

Pressure of fluid in both pipes is same, then why velocity of fluid coming out of 3 million Km long pipe is less than that in 3 centimeter long pipe? Answer is friction of fluid with pipe. But if the fluid is not moving in entire length of pipe at exactly same moment we open valve, then how the fluid near valves calculate friction of entire length of pipe and decide its velocity?

(6) Let L = length of pipe, a = area of pipe, v = velocity of fluid coming out of pipe and c = velocity of pressure waves. Consider that we have opened the valve of pipe and fluid begins to flow out. This information reaches to fluid level in reservoir after time t where t = L/c. But during this time interval t, fluid is flowing out of pipe. Hence volume of fluid flown out = avt = (avL)/c. That means volume of fluid equal to (avL)/c was compressed in this pipe of length L. This is tremedous amount of fluid. Compressibility of any fluid just can't be such large.

(7) We can carry out simple experiment to verify that information regarding opening of valve i.e. flow of water must reach to water level in reservoir instantaneously. There are lot of pipelines connected to reservoir (Dam or something like that). Let length of this pipeline be 30 Km. At outlet B, hose pipe is attached. Consider that water is flowing in this system under gravitational field. If we lift hose pipe at outlet B, we will note that velocity of water coming out of hose is decreased at exactly same moment. If established knowledge of fluid dynamics is correct, then velocity of water coming out of hose must not decrease for about 20 seconds until pressure waves reaches to water level in reservoir.

If we could lift the hose pipe equal to height of water level in reservoir in say 5 seconds, then we will find that flow of water through hose pipe and reservoir stops completely the moment height of water column in hose equal height of water column in reservoir. If reader say that water will continue to flow for another 15 seconds, then as shown above in analysis section, we can lift the hose pipe to a height greater than that of water level in reservoir. As water will continue to flow out at greater height, it will have higher potential energy than it had in reservoir. This will be free energy because we have not spent any energy to lift that water to greater height.

(8) To support Author's claim that mistake is done during course of history, I am giving below example relating to different branch of Physics.

Example: I request reader to take ride on bicycle on rainy streets. Let velocity of bicycle + you be v. Suppose that if you throw small stone with velocity v in the direction of motion of bicycle, then velocity of stone with relative to you will be v but with relative to pedestrian, it will be v + v = 2v. If you throw stone with same velocity opposite to direction of motion of bicycle, with relative to you will be v, but with relative to pedestrian, it will be v - v = 0.

Now look at the front wheel. Linear velocity of tyre of wheel is v (because that is why bicycle is moving with velocity v). As you are on rainy street, some mud will stick to tyre of bicycle and as tyre is rotating, mud is also roating with tyre.

Now when this mud is thrown in tangential direction, what will be its velocity with relative to you? If you say that velocity of bicycle will add to velocity of mud, then velocity of mud in the direction of bicycle with relative to pedestrian should be v + v = 2v and with relative to you, it should be v. That means, mud should escape from tyre of front wheel and travel before your eyes with velocity v. Are you seeing mud escaping and flung before your eyes (in the direction of bicycle) with velocity v?

(9) When we pull one end of one lightyear long rod, physicists say that this information will travel to other end with speed "less than light". Why physicists can't give figure of speed? Does this information travel with sound velocity? if yes, then when, where, who, how it has been experimentally verified? If it is not experimentally verified, then on which basis physicists make such claim?

(10) When the existence of "gravitational waves" has been proved?

Conclusion: After carefully studying the fluid flow analysis, we should come to the conclusion that information regarding uninterrupted, free flow of fluid under gravitational field must travel back to fluid level in reservoir at exactly same moment. Otherwise law of conservation of energy is violated. __________________________________________________ ____

Postal Address: Mr. Abhijit B Patil, C/o LIC of India, At/Po/Tq: Shahada City, Dist: Nandurbar, Maharastra State, INDIA. Pin: 425 409. __________________________________________________ _

 Wen Long June 30, 2002 12:57

Re: Terrible Mistake In Fluid Dynamics History

Abhi:

I think your basic assumption is incorrect:

When we OPEN the valve of garden hose connected to water reservoir at greater height, with hose full

of water, water begins to flow out due to gravity. Established knowledge of fluid dynamics states that this information

travels across full length of hose pipe back to water level in reservoir through pressure waves with appropriate acoustic

velocity in hose pipe. When these pressure waves reach to water level in reservoir, only after that water level comes

down. This is not true. If it is true, then we can use this time interval of information transfer to create "free" energy.

My comment:

You are assuming that the water in the hose have to flow out after the pressure wave reaches the reservoir. But the first drop of water flowing out will be compensated by the density change, and the density change/pressure_wave will THEN propagate back to the reservoir with sound speed. Means sound waves are generated "after" the first drop of water flow out. So it should reaches the reservoir later after the water flow out.

About your arguments on energy conservation mgH>mgh, you are only considering gravitational potential energy. While the compressibility of fluid gives internal energy like a spring. If you let go a compressed spring in vertocally upward direction, the spring end moves immediately, does that mean the spring gains gravitational potential energy without compensation? Surely not. The compensation comes from the stored energy when you compress it.

Wen

 Jim Park June 30, 2002 21:44

Re: Terrible Mistake In Fluid Dynamics History

Wow! Wouldn't this make a great question for a doctoral oral qualifying exam? Imagine it would have the examining committee arguing among themselves.

 wen long June 30, 2002 22:08

Re: Terrible Mistake In Fluid Dynamics History

I forgot to say one thing,

The gravity is doing work and putting energy in both fluid motion and internal energy.

Wen

 wen long June 30, 2002 22:23

Re: Terrible Mistake In Fluid Dynamics History

Yeah!, it's too harsh a question and can take forever for the committee members to argue @ @

Jim wrote:

Wow! Wouldn't this make a great question for a doctoral oral qualifying exam? Imagine it would have the examining committee arguing among themselves.

 Pete July 1, 2002 08:41

Re: oral exam question

I actually had such a question on the oral part of my Ph.D. qualifying exams. Not to the thorough details mentioned here, but the same basic premise and issues.

And yes it was harsh....

 Abhi July 1, 2002 09:28

Re: Terrible Mistake In Fluid Dynamics History

Dear Dr. Wen,

I really don't understand why people around the world are unable to give answer of my following question.

"It is "assumed" that what happens to flowing fluid after CLOSURE of valve must happen to steady fluid(having only PE) when we OPEN the valve and then to uninterrupted flow of fluid. And this "assumption" is being treated as "truth" and NEVER at any time in history has been experimentally verified.

If reader believe that it is experimentally verified then when, where, who, how?"

I have asked this question to thousands of scientists, preofessors, people through emails and message boards like this. But till today no one has given answer.

Will you please try to understand my position?

-Abhi

 Abhi July 1, 2002 09:36

Re: Which question? (oral exam question)

Dear Dr. Pete,

Can you please tell me which question was asked to you and what answer you gave?

-Abhi

 Pete July 1, 2002 10:02

Re: Which question? (oral exam question)

It was over a year ago, I can't seem to remember all the details and responses. The experience was a bit of a blur.

Basically I was asked to draw the hose attached the bottom of a large tank or reservoir, and asked just generally what happens upon opening a valve at the end of the hose.

I recall the committee asked me to express the mass flow rate as a function of time and the height of fluid in the tank as a function of time. Some of the discussion involved a 1-D momentum analysis given the hydrostatic pressure at the bottom of the tank and the ambient external pressure.

 Wen Long July 1, 2002 15:25

Re: Terrible Mistake In Fluid Dynamics History

Abhi:

"It is "assumed" that what happens to flowing fluid after CLOSURE of valve must happen to steady fluid(having only PE) when we OPEN the valve and then to uninterrupted flow of fluid. And this "assumption" is being treated as "truth" and NEVER at any time in history has been experimentally verified.

My understanding of you question is: Your are inquiring an asumption:

a) Dynamics of flow happens in the course of closing a valve to a flowing system and the flow finally stoped and become still(no motion)

will equal to

b) Dynamics of flow happens in the course openning a valve to a still system and the flow develops to stable status.

This is an "arrow of time" problem, time can only go forward, but can't go backward. While all our classical mathematical description(equations) of mecanical system can give solution backward. Means a physical phenomenon should be able to happen backward without violating the equations we got when set t=-t. Just like water can dash down a hill, and it should be able to go back in the same manner if we turn the "arrow of time" backward.

a) and b) I wrote in the upper lines are the same in terms of mathematical description. Only if we can make a t'= -t coordinate transform to the equation. That's why people "assume" the results will be the same.

While in reality, people can never turn back time arrow and not able to do experiments for this. This is a deep problem not in classical theory. It roots in the phylosophical understanding of time and space. Time channels only occur in scientific fiction now. It's still not well understood and certainly beyond my ability to address.

The good point is you are very thoughtful, but you may not realize the difficulties involved in these problems. Please carry on, and we expect you'll be a great guy in the future.

Read books of Stephen W. Hawkin's books may be helpful:

http://www.hawking.org.uk/home/hindex.html

Wen

 Abhi July 2, 2002 13:22

Re: Help On Fluid Flow Calculation

Dear Dr. Wen,

Let height of Dam full of water be 10 meter. Let length of pipeline attached to bottom of Dam be 100 Km and let cross sectional area of pipe be 1 square meter.

(1) Can you please calculate velocity of water flowing out when we open the valve at outlet B?

(2) How much time it will take to decrease velocity of water to zero?

(3) And how much water will flow out until pressure waves reaches to inlet A?

(4) After velocity of water decreases to zero, is it so that water will not flow untill pressure waves reaches to Dam?

And most importantly, is there someone in this discussion forum who work or access to a project in which long water pipelines are involved?

Hoping that your answers will end my dilemma.

Thanking you,

-Abhi

 Jonas Holdeman July 6, 2002 11:22

Re: Terrible Mistake In Fluid Dynamics History

The problem with "questions" of this type is that they make some idealized assumptions, but then ask questions about non-idealized conditions. A classical problem that comes to mind is "What happens when an irresistible force meets an immovable object?" Irresistibility and immovability are useful idealizations, but neither can be realized and together they are contradictory.

Incompresssible flow is a limiting behavior of many natural flows. An incompressible fluid is an idealization beyond experience and its behavior must be examined in its own context. The closest thing to incompressibility in nature might be the core of a neutron star, but no one has experienced this either, except in their imagination (real or virtual).

If one considers the hypothetical case of an incompressible fluid in a rigid pipe, then pressure disturbances would propagate at infinite speed (violating causality in the process). If one assumes that the flow of such a fluid in such a pipe were closed off at the outlet, the effect would be felt instantly at the inflow point. Incompressible fluid, rigid pipe, instant closure, Newton's law -- valid idealizations on their own -- are mutually contridictory when taken together.

In a real situation, the fluid is compressible and the pipe non-rigid. When a valve is opened at the outlet, the local pressure drops, the fluid expands, the pipe volume contracts and fluid starts to flow immediately (though perhaps at a slow rate). When the pressure wave reaches the reservoir, the slug of fluid in the pipe accelerates until the pressure difference is balanced by the viscous forces. This reverses when the valve is turned off.

Hopefully we don't experience these details in our lives. Air cushions are installed near the valves which serve as source and sinks as water flows in and out of the cushions, providing instant water and stopping flow gradually by their compressibility. If someone lives in a house where the plumbing is not securely attached to the interior of the walls and with no cushions, one hears the rattleing of the pipes as the water is turned on and off. This is the "water hammer" effect. I mention this because plumbing systems have been engineered to mitigate some hydrodynamic problems in such a way that they do not become part of our everyday experience.

For the most part, the laws of fluid motion are consistent and well-tested, and one should examine one's reasoning carefully and consistently before declaring them a terrible mistake. That said, there is something strange about the incompressible Navier-Stokes equation...

 alexy July 8, 2002 09:11

Re: Terrible Mistake In Fluid Dynamics History

Hey Jonas, as good as always:) --alexy.

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