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Field Nature of Fluid Mechanics

Field Nature of Fluid Mechanics. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi. Description of the Fundamental & Distributed source of Actions……. How can a force occur without any countable finite bodies & apparent contact between them?.

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Field Nature of Fluid Mechanics

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  1. Field Nature of Fluid Mechanics P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Description of the Fundamental & Distributed source of Actions……

  2. How can a force occur without any countable finite bodies & apparent contact between them? Major Question to be Answered in Fluid System "action at a distance" has stymied many of the great minds

  3. Every Field is an Abstract Painting

  4. The Surprising Actions in Fluid systems • Compared to solids fluids seem almost alive, magical. • They flow, change form to accommodate the surroundings, produce gurgling sounds, and refract light to produce shimmer. • There are few things that can match the majesty of a waterfall or the wind. • What causes (Primarily) fluids to flow? • As with solids, motions can only be produced by unbalanced forces so what is the nature of the forces in a fluid?

  5. How A Force is Created ??? • Newton developed the theories of gravitation in 1666, when he was only 23 years old. • Some twenty years later, in 1686, he presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis.“

  6. Think about Field • Let's focus on Newton's thinking. • Consider an apple starting from rest and accelerating freely …... • Until the apple hits the ground, the earth does not touch the apple so how does the earth place a force on the apple? • Something must go from the earth to the apple to cause it to fall. • The force of the earth's attraction causes the apple to fall, but how specifically? • The earth must exude something that makes acceleration of apple. • This something exuded by the earth was called as the gravitational field. • We can start by investigating the concept called field. • The force of the earth's attraction causes the apple to fall, but how specifically?

  7. The Concept of Field • Something must happen in the fluid to generate/carry the force, and we'll call it the field. • Few basic properties along with surroundings must be responsible for the occurrence of this field. • Let this field be . • "Now that we have described this field, what force would this field place upon my system.“ • What properties must the fields have, and how do we describe these field?

  8. Advanced Fluid Flows for Post Graduate Students • Correctly balancing the physics and mathematics is the important educational aim. • By pushing it to extremes one may end up in a course of descriptive presentation, rules of thumb and table or graph • readings fit for conventional routine jobs only. • It is then far from what one might expect from a graduate engineering course. • On the other hand, little application and a very big mathematical apparatus may feature a kind of theoretical physics which should not be the goal when training Thermal Scientists/Engineers.

  9. Educational Aim of Teaching Viscous Fluid Flows • To demonstrate when and how deep an engineer is bound to dive into the problem, where he should use exact mathematical methods and where approximations. • To use the proper numerical apparatus, a pocket or desk calculator if a calculator is justified, or a thoroughly checked computer program if the problem requires it. • To offer ample opportunities and utilise them consciously.

  10. Fields & Properties • The fields are sometimes described as scalar and sometimes vector or both in nature. • There are special vector fields that can be related to a scalar field. • There is a very real advantage in doing so because scalar fields are far less complicated to work with than vector fields. • We need to use the calculus as well as vector calculus. • Study of the physical properties of Scalar & vector fields is the first step to attain ability to use Fluid Flow Analysis. • An Ultimate Imagination of A Dynamic Painting!!!

  11. Define mother by Studying the Child • Start from the path integral Work: • Conservative Vector Field The energy of a Flow system is conserved when the work done around all closed paths is zero.

  12. Mathematical Model for Field • For a function gwhose derivative is G: the fundamental lemma of calculus states that where g(x) represents a well-defined function whose derivative exists.

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