Experimentals: Examples of Bernoulli's theorem

RUBEN: Good evening and welcome to This Is Your Theorem. Tonight we honour the great Swiss scientist Daniel Bernoulli who can't be with us tonight because he's dead. Bernoulli died in 1782, but he was some genius, as many of us know.

BERNIE: Bernoulli's theorem explains the strange behaviour we see when gases and liquids flow, some examples of which we'll see tonight. Wow.

RUBEN: So without any further do, Daniel Bernoulli, this is your theorem.

BERNIE: Bernoulli was educated in Switzerland, a tiny country where people wear clothes like this, eat cheese like this and where pocket knives have more accessories than you can poke a stick at. In 1725, Bernoulli moved to St Petersburg. And while his friends were back home yodelling, it was in St Petersburg that Bernoulli made his breakthrough.

RUBEN: No-one can be sure, but perhaps it was one of these that sparked Bernoulli's curiosity.

BERNIE: The water pouring down ought to keep an egg at the bottom of a glass, but instead it rises to the surface. Freaky, hey?

RUBEN: One can see why Bernoulli was intrigued, but it's not just his seminal work on eggs and water that made him famous. Bernoulli's work also had serious implications for balloons. Commonsense suggest that blowing between these balloons would cause them to move apart. But instead the opposite happens and they come together - bizarre.

BERNIE: Bernoulli discovered that the pressure of moving air is lower than the pressure of air that's still. The faster air moves, the lower its pressure. It might sound like regular physics mumbo jumbo, but Bernoulli's theorem is great because things always do the opposite of what you'd expect.

RUBEN: Like the liquid in this straw. When you blow across the top of a straw you'd expect the air to go down the straw and push the cordial down. But Bernoulli's theorem says that the air that's blown across the top is at a lower pressure. So it acts as though you were sucking on the straw. And look what happens - cordial is rising up the straw. That balloon - what a genius. But its brilliance didn't stop there.

BERNIE: If we put a balloon in the air stream of this hair dryer you might expect the balloon to go flying up and then fall back to the ground. But instead the balloon is trapped by the fast-moving air from the hair dryer, which, according to Bernoulli's theorem, is at a lower pressure than the still air around it. Once again, the balloon does the opposite of what you'd expect.

RUBEN: Here's a challenge Bernoulli would never have fallen for. Try blowing a ping-pong ball out of a funnel. You'll find it's impossible. Why? Because fast-moving air surrounds the ball and fast-moving air has lower pressure. The ball is trapped. And, look at this, the balls stays trapped even if you hold the funnel upside-down. Once again, the opposite of what you'd expect.

BERNIE: Yes, Bernoulli's work has changed lives the world over. Thanks to Bernoulli's theorem...

RUBEN: ..eggs can impress other breakfast foods by floating in running water...

BERNIE: ..hair dryers and balloons can live together in harmony...

RUBEN: ..and the humble ping-pong ball can resist the mightiest set of lungs.

BERNIE: (In falsetto) You can huff and puff, but you'll never blow me out.

RUBEN: So Daniel Bernoulli, this is your theorem.