by Ferdinando Catalano
(passing through arteriosclerosis)
When I was a boy in the ‘60s and ‘70s, it was normal to take a shower in the bathtub with a vintage curtain that almost turned it into a little cabin. A strange thing happened: while the water flowed down, the curtain would stick to your thigh (if you are young and use luxurious shower enclosures, ask your parents). Curses! The first time it happens you think, “I left the bathroom window open!” But a quick peek reveals the window is closed after all. The door is shut tight, as well. So what could be the cause?
If you were a more pragmatic sort, such esoteric oddities may not have concerned you, and you could have finished washing in peace. But if you were like me, and a little more curious, then your ignorance of physics would not have stopped your speculation: “Was it my presence that caused it? Was it the soap, or perhaps the water?”
These questions were destined to remain unanswered until I went to university, and discovered studied Bernoulli’s principle. No teacher revealed this mystery to me, but, to my great satisfaction, I stumbled upon it by deduction. This law of physics, in essence, explains that when the speed of a fluid (liquid or aeriform) increases, its pressure decreases. It can be derived from that most sacred principle among physicists, the law of conservation of energy, which is how I discovered it..
Let’s go back to the curtain. When the water is off, the pressure of the air in the room is the same both inside the shower cabin and outside. But when the tap is opened, water flows into the shower, and the speed of the liquid creates a decrease in pressure inside in accordance with Bernoulli’s principle. Therefore, the pressure outside the cabin becomes greater than that on the inside. Thus the curtain is pushed inwards and sticks to your thigh.
At the age of 60, I discovered at my own expense that there is also another application of this physical law in medicine.
Do you know when you put your thumb over the opening of the water hose while watering the garden plants? The water comes out of the nozzle with greater speed and goes further. You do it on purpose, but if you ask why, 9 out of 10 people will tell you that this is the case because there is more pressure. This is, in fact, the opposite of what happens, and illustrates well that sometimes common sense and physics don’t seem to agree.
Recall that Bernoulli says where the speed of a fluid increases, its pressure decreases.
This effect takes a sinister turn in the human body: when cholesterol builds up inside your arteries past a certain point, it is just like putting your thumb over the mouth of the hose; the speed of the blood inside the artery increases. Now if the blood velocity increases then the internal pressure must necessarily decrease. Thus, the external pressure can eventually exceed the internal pressure, causing the artery to close wholly or in part. Unfortunately, the results of this are easy to predict…
Let’s get to the planes. Think of the profile of a wing or look at it well in the figure. Imagine the two of us are two air molecules at the top of the wing profile and we decide to separate and meet back at the exact same time. I pass over and you go down. Again, carefully consider the geometry of the profile. Which of us has had to travel the greater distance? Of course the answer would be me. And which one of us went faster? Also me, given that I covered more ground in the same time. Then the air velocity above the wing must be greater than the air velocity below the wing.
For this we can once again thank Bernoulli. The air pressure is lower above the wing and therefore the pressure under the wing pushes upwards just as the external pressure pushed the shower curtain against your thigh.
And yet, for all his contributions to the field of fluid dynamics, Bernoulli’s story ends on a sad note: when Daniel Bernoulli discovered this very important law governing the dynamics of fluids, his father, Johann, who was himself a great mathematician whose skill was exceeded only by his ego, was so envious that for the rest of his days, he never spoke to his son again.
- Make a strip of paper, 4cm x 20cm, and hold one end between your thumb and forefinger. Obviously, it bends down. Now blow on it horizontally. What happens?
- Get two empty Coca Cola or beer cans and put them on a very smooth surface, such as glass. Place them without touching, perhaps 1 cm from each other. Now, ideally with a straw, blow between them. What happens?
If I managed to help you understand Bernoulli’s law, it is because you already knew of it, you simply did not know why. But you could impress your friends who still wonder why the curtain sticks to their thigh.
Hello to everyone, Ferdinando.
Drawing by: Alessandro Perina