Piston Engines - Introduction — Page 10, Lesson 14

Let's start with the Venturi tube, because it's the practical bridge between Bernoulli's theorem and the engine you'll be studying. A Venturi tube is sometimes called a convergent/divergent duct. Look at its shape: it has an inlet that narrows down to a throat, and then an outlet section that is relatively longer and increases in diameter towards the rear. So it squeezes in, and then opens back out. Now, why does that matter? It comes down to something called the continuity equation. For a flow of air to remain streamlined, the volume passing a given point in unit time — that's the mass flow — must remain constant. If you position a Venturi tube in an airstream, then for the air to stay streamlined, the mass flow through the Venturi must stay constant. And here's the key relationship: mass flow is dependent on Area × Density × Velocity, and it is a constant. That's the continuity equation. So if the air has to pass through the reduced cross-section of the throat, and the mass flow must stay constant, then the speed of flow through the throat must increase. And here's where Bernoulli's theorem comes in: that increase in speed brings about an accompanying pressure drop and a temperature drop. So you get a low-pressure, low-temperature region right at the throat. This isn't just theory. Venturi tubes have many applications in aircraft systems. For example, the pressure drop at the throat of the Venturi forms the basic principle of operation of the carburettor — that's covered in Chapter 8. So keep this shape in mind; it's the heart of how fuel gets drawn into the engine. Now let's move to the gas laws, because these govern what happens inside the cylinder. First, Boyle's Law. It states: in a gas held at a constant temperature, the volume is inversely proportional to the pressure. In equation form, P × V = K, where P is the absolute pressure of the gas, and V is the volume occupied when the pressure is P. So the product of absolute pressure and volume of a given quantity of gas is constant, as long as the temperature doesn't change. Squeeze the gas, volume goes down, pressure goes up — the product stays the same. Next, Charles's Law, also called Gay-Lussac's Law. It states: if any gas is held at a constant pressure, its volume is directly proportional to the absolute temperature. In equation form, V divided by T equals K. So heat the gas, it expands; cool it, it contracts — at constant pressure. Now, the Combined Gas Law is exactly what it sounds like — a combination of Boyle's and Charles's laws. It represents the relationship between Volume, Pressure, and Temperature all at once. It can be shown as P × V divided by T equals K. Alternatively, where K is the gas constant, P × V = K × T. Or, comparing two states of the same gas: P1 × V1 divided by T1 equals P2 × V2 divided by T2. That last form is the one you'll use to track what happens as conditions change inside the cylinder. So how does this apply to the engine? The changes in pressure, volume, and temperature within the engine cylinder as the piston moves between the top and the bottom of its stroke are exactly what the Combined Gas Law describes. These movements are known as the four strokes of an internal combustion engine — internal because combustion takes place in the engine cylinder, not externally as in a steam engine. This is explained in the Otto cycle text that follows. Here's the important part: only one useful, or power, stroke is available during the cycle, and that cycle occupies two revolutions of the crankshaft. So the piston moves up and down the cylinder four times — that's four strokes — but theoretically, there are actually five events in the cycle. Keep that in mind: four strokes, two crankshaft revolutions, one power stroke, and five events. We'll unpack those events when we get into the Otto cycle proper.