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

Creation of An important Field for Survival of LIfe Morowitz [1992]

An Important Field by Nature

How to Create Force??? 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.“

The question we need to answer is how can a force occur without any countable finite bodies & apparent contact between them? "action at a distance" has stymied many of the great minds

What is a Field????

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?

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 found this field, what force would this field place upon my system.“ What properties must the fields have, and how do we describe these field?

Fields & Properties The fields are sometimes scalar and sometimes vector 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 vector fields is the first step to attain ability to use Viscous Fluid Flow Analysis.

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

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

The mother of Vector Field There are integrals called path integrals which have quite different properties. In general, a path integral does not define a function because the integral will depend on the path. For different paths the integral will return different results. In order for a path integral to become mother of a vector field it must depend only on the end points. Then, a scalar field  will be related to the vector field F by

The Engine : An agent to generate Force

The Birth of A Special Operator In order to justify the Cartesian system of description, the fundamental Lemma states that;