Nature of (FIRE)

Mechanics. - ppt video online download : Cartesian Coordinates Normal space has three coordinates. x1, x2, x3 Replace x, y, z Usual right-handed system A vector can be expressed in coordinates, or from a basis. Unit vectors form a basis x3 x2 x1 Summation convention

Tensors. Jacobian Matrix  A general transformation can be expressed as a matrix. Partial derivatives between two systemsPartial derivatives between two. - ppt download : Covariant Transformation  The components of a gradient of a scalar do not transform like a position vector. Inverse transformation  This is a covariant vector. Designate with subscripts  Position is a contravariant vector. Designate with superscripts

Powerful tool For Effective study and to Understand Flow Devices…… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Tensor Notation. - ppt download : Introductory Remarks The tensor Notation is a powerful tool that enables the reader to study and to understand more effectively the fundamentals of fluid mechanics. Enables to recall all conservation laws of fluid mechanics without memorizing any single equation. The quantities encountered in fluid dynamics are redefined as tensors.

Operators. 2 The Curl Operator This operator acts on a vector field to produce another vector field. Let be a vector field. Then the expression for the. - ppt download : 3 The physical significance of the curl operator is that it describes the “rotation” or “vorticity” of the field at the point in question. It may be regarded as a measure of how much the field curls around that point. The curl of is defined as an axial ( or rotational) vector whose magnitude is the maximum circulation of per unit area as the area tends to zero and whose direction is the normal direction of the area when the area is oriented so as to make the circulation maximum. where the area is bounded by the curve L, and is the unit vector normal to the surface and is determined using the right – hand rule.

Tensors Part C Tensor Calculus 2C1 Tensor-valued functions of a tensor - ppt download : Tensors Show that:

Statistical Mechanics - ppt video online download : Statistical distributions- Maxwell-Boltzmann statistics – Distribution of molecular energies in an ideal gas-Average molecular energy- Equipartition theorem Maxwell-Boltzmann speed distribution law- Expressions for rms speed, most probable speed and mean speed