Fluid Mechanics and Hydraulic Machines

APPENDIX A

Review of Mathematical Concepts

A1 Vector Algebra, Calculus and Integrals

Vectors and tensors have provided a great relief in mathematical analysis of fluid flow through or around the bodies and therefore some space is provided here to recapitulate their important aspects. The quantities like, mass, density, temperature, energy are scalar quantities. For scalar quantity, knowledge of the magnitude is enough to describe that quantity. The velocity and forces are the vector quantities because the information about the direction in which these act is also needed in addition. Thus a vector has both magnitude and direction. These have unique components when resolved along the reference axes which change with rotation of the axes. However, ...