Basic Aerodynamic Theory

The Principle of Continuity

One of the fundamental laws of the universe is ENERGY and MASS can neither be created nor destroyed, only changed from one form to another. To demonstrate the effect this basic Principle of Continuity has on aerodynamic theory, it is instructive to consider a streamline flow of air through a tube which has a reduced cross-sectional area in the middle.

The air mass flow, or mass per unit time, through the tube will be the product of the crosssectional area (A), the airflow velocity (V) and the air density (ρ). Mass flow will remain a constant value at all points along the tube. The Equation of Continuity is:

A × V × ρ = Constant

Because air is a compressible fluid, any pressure change in the flow will affect the air density. However, at low subsonic speeds (< M 0.4) density changes will be insignificant and can be disregarded. The equation of continuity can now be simplified to: A × V = constant, or:

Basic Aerodynamic Theory 3

Theory Aerodynamic Basic

Note: An ideal fluid is both incompressible and has no viscosity.

This statement can be expressed as: Pressure + Kinetic energy = Constant or:

p + 1/2 ρ V2 = Constant

Consider a mass of air: Static Pressure 101 325 N/m2, Density 1.225 kg/m3 and Velocity 52 m/s, its dynamic pressure will be: 1656 N/m2. [Q = ½ × 1.225 × 52 × 52]

Pressure (101 325 N/m2 ) + Kinetic energy (1656 N/m2 ) = Constant (102 981 N/m2 )

Figure 3.2 Bernoulli’s Theorem

Because the velocity of air at the throat has doubled, its dynamic pressure has risen by a value of four, and the static pressure has decreased. The significant point is that:

Static Pressure + Dynamic Pressure is a constant. This constant can be referred to either as:

TOTAL PRESSURE, STAGNATION PRESSURE or PITOT PRESSURE.