Time Vs Energy Mr. Abhijit Patil, C/o LIC of India, Shahada, Dist: Nandurbar, (MS), India. Pin: 425409.

Abstract: This article deals with instantaneous (superluminal) transmission of information of fluid flow under gravitational field..

Introduction: Consider a garden hose pipe through which there is steady flow of water due to Gravity. If we lift this hose pipe straight upward, pressure rises at bottom of hose due to gravity. Established knowledge of fluid dynamics states that this information regarding rise in pressure will be communicated to water level in reservoir through pressure waves with acoustic velocity. This article aims to prove that this information must be communicated to water level in reservoir instantaneously. Otherwise law of conservation of energy is violated.

Fluid Flow Analysis Under Gravitational Field: Consider a reservoir A of volume U 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 A. At outlet B, there is vertical empty pipe of height H where H = h + x and H > h opening in another reservoir B at height H of volume U. Let " a " be cross sectional area of horizontal pipe of length L and that of vertical pipe of height " H ". Volume of vertical pipe is much less than volume U of both reservoirs A and B, hence can be neglected. 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 U = avt = (avL)/c

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 horizontal pipe through 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 steady flow of water. After time t = t, U volume of fluid has entered in closed pipe system of horizontal pipe of length L. Hence only way to accommodate this U volume of fluid is vertical pipe of height H and then reservoir B. Hence there will U volume of fluid in reservoir B 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 reservoir B at 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?

If we say that fluid level in vertical pipe will never rise above height h, then it means volume of fluid equal to (avL)/c, which has flown in horizontal pipe through inlet A during time interval t, will be compressed in this horizontal pipe of length L. This is tremedous amount of fluid. Compressibility of any fluid just can't be such large.

Conclusion: After carefully studying the fluid flow analysis, we should come to the conclusion that information regarding rise in pressure due to gravity at outlet B must travel back to fluid level in reservoir at exactly same moment. Otherwise law of conservation of energy is violated. __________________________________________________ ____

Author: Mr. Abhijit Patil, C/o LIC of India, Shahada, Dist: Nandurbar, (MS), India. Pin: 425409. __________________________________________________ _____

If you are going to refer to conservation of energy you need to include all forms of energy: potential energy of fluid (height), kinetic energy of fluid (velocity) and internal energy (in this case related to how compressed the fluid is). The sum of all these should be conserved and is if you do it correctly.

Dear Dr. Pete,

I apologize all of you. I have done terrible mistake while understanding this problem. I am totally wrong on this article or previous versions of the same article.

Thanks for your reply.

-Abhi.