1 / 12

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?.

aaronsauve
Download Presentation

Field Nature of Fluid Mechanics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related