We're starting a new chapter now — Chapter 3, Basic Aerodynamic Theory — Page 44, Lesson 52

We're starting a new chapter now — Chapter 3, Basic Aerodynamic Theory. And I want to begin with the very foundation, the Principle of Continuity. Here's the core idea: one of the fundamental laws of the universe is that energy and mass can neither be created nor destroyed — they can only be changed from one form to another. That's the Principle of Continuity. To see what this does to aerodynamics, imagine a streamline flow of air moving through a tube that has a reduced cross-sectional area in the middle — a constriction, a throat. Now, the air mass flow — that's the mass of air passing a point per unit time — through that tube is the product of three things: the cross-sectional area, which we call A; the airflow velocity, which we call V; and the air density, which we call ρ, the Greek letter rho. And here's the key: mass flow remains a constant value at all points along the tube. So the Equation of Continuity is A × V × ρ = Constant. Now, air is a compressible fluid, so any pressure change in the flow will affect the air density. But — and this is an important limit — at low subsonic speeds, below Mach 0.4, density changes are insignificant and can be disregarded. So below M 0.4, we can simplify the equation of continuity to A × V = constant, or put another way, Velocity V equals the Constant divided by the Area A. Let me make that concrete with the numbers from the figure. Imagine the tube with a full cross-sectional area of 1 cubic metre, and air flowing through at 52 metres per second — that's 100 knots. The mass flow is 52 cubic metres per second. Now the tube narrows to half a cubic metre. Because mass flow must stay constant at 52 cubic metres per second, the velocity must double — it becomes 104 metres per second, which is 200 knots. Then the tube widens back out to the full 1 cubic metre, and the velocity drops back to 52 metres per second, 100 knots. So the takeaway: because mass flow must remain constant, a reduction in the tube's cross-sectional area results in an increase in velocity, and vice versa — an increase in area gives a decrease in velocity. That's the whole principle in one sentence. And why does this matter for a pilot? Because the equation of continuity lets us predict mathematically the velocity changes of airflow around a given shape — below Mach 0.4. That's the foundation we'll build on next, because velocity changes are exactly what Bernoulli's Theorem is about.