Recently, a group of students at Purdue University used a simple device to make a ping-pong ball break the speed of sound. But that's not the coolest part. The device they used, called a de Laval nozzle, is actually centuries old. It's no exaggeration to call this the gadget that made the industrial revolution possible — and the space age, too.
De Laval steam turbine photo via Practical Machinist.
This video shows you exactly how much damage a ping-pong ball can do. A little air compression, a little vacuum, and a well-shaped nozzle, and a ping-pong ball can break the sound barrier and shoot through four soda cans on its way across the room. It can also break through a ping-pong paddle, which makes me want to see what kind of damage it does to a human hand, even if I'm not going to volunteer my own. The students who built the ping-pong ball gun did it by sticking a ping-pong ball in one tube, covering both sides of the tube, and pumping all the air out. They then attached another tube to the first - with a nozzle in between - and pumped air in to it until the pressure caused the barrier between the two tubes to collapse and the ping-pong ball to get pushed out on a supersonic wall of air.
When calculating how fast the ball should go, it's natural to assume that the main factor will be the pressure of the air in the first tube, the lack of pressure in the second, and the diameter of both. These play into the acceleration of the ping-pong ball, but it turns out that what really makes the difference is the nozzle between the tubes.
The de Laval nozzle is also known as a convergent-divergent nozzle, and it's a simple device that not only makes the difference between a subsonic and supersonic ping-pong ball, but the also makes the difference in the industrial revolution and the space age. You'll notice that, even on cartoon rockets, the exhaust pipes are not straight. They pinch inwards and then flare out again, like an hourglass. This is not just a stylistic touch.
During the industrial revolution, people wanted to accelerate gases like steam in order to have them drive engines or turbines. It was common sense to make the tubes through which the gas flowed pinch inwards and become smaller. Everyone has seen the way water accelerates as it goes from a wide stream to a narrower one. But the process became one of diminishing returns. Although the gas would accelerate, at a certain level the flow would just be choked off. No matter how thin the tube, and how much pressure built up behind it, there was little or no further acceleration. Engineers attempted to get around this by making changes to the texture, size, and tapering of the tubes, but nothing worked. Until, in 1888, Gustaf de Laval came up with a new nozzle that tapered down, like all the rest, and then flared outwards again. Suddenly gas was shooting out at incredible rates, much faster than it ever had before.
The engineers of the industrial revolution had at last discovered the fact that materials can behave very differently under different conditions. Gas that is moving at subsonic speed behaves differently when it moves at supersonic speed. At subsonic speed it behaves the way we see water behave in narrowing rivers. As its container narrows, it moves faster. If you were to sit by the side of a river at one section and calculate the amount of water that went past you, and went downstream to a narrower section and calculated again, you would find that the overall volume of water that passed you by both times was the same. As the stream narrows, its speed increases and the mass flow rate is kept constant. The same happens in a narrowing tube full of gas, until the gas reaches the speed of sound. That's the choke point - the gas doesn't go any faster, even if the tube gets narrower and narrower.
The de Laval nozzle tapers down, forcing gas to go faster and faster until it reaches the speed of sound. At the speed of sound, the conventional wisdom reverses itself. Instead of a narrower tube making the gas go faster, widening the tube makes it go faster. Flaring the nozzle out again causes the pressure on the gas at the choke point to dissipate and the gas to accelerate even faster than the speed of sound. It's like a spring that has been pushed down and then released, all that energy from the pressure changing into speed. And all of that released energy moves in only one direction - shooting outwards at above the speed of sound.
This supersonic gas is what pushes the ping-pong ball so fast that it can tear through aluminum and wood. It was also what allowed the V-2 rocket, which was designed by Germany as a bomb and then used by America as an early vehicle for space research, to fly through the sky. It remains on jet engines to this day, shooting things through the sky, and through space. And all it takes is an hourglass shape.
Read more via arXiv