Conceptual Aircraft Design

Appendix CFundamental Equations (See Table of Contents for Symbols and Nomenclature.)

Some elementary yet important equations are listed here. Readers must be able to derive them and appreciate the physics of each term for intelligent application to aircraft design and the performance envelope. The equations are not derived here – readers may refer to any aerodynamic textbook for their derivations.

C.1. Kinetics

Newton's Law: applied force, F = mass × acceleration = rate of change of momentum.

force = pressure × area and work = force × distance.

Therefore, energy (i.e. rate of work) for the unit mass flow rate m is as follows:

Steady state conservation equations are as follows:

C.1

C.2

With viscous terms, it becomes the Navier–Stokes equation. However, friction forces offered by the aircraft body can be accounted for in the inviscid flow equation as a separate term:

C.3

From the thermodynamic relation for perfect gas between two stations gives

C.4

C.2 Thermodynamics

Using perfect ...