Last time we saw how just one liter of water could build up enough pressure to burst a large glass barrel. The key factor was the height of the water. When poured into a long thin straw the 1 liter reached a height of around 75 ft, creating a pressure inside the barrel of around 45 pounds per square inch. In other words, each square inch of the glass felt a force of 45 pounds pushing it outwards. But here's the paradox: How could just two pounds of water create a pressure of 45 pounds per square inch? This law that the pressure depends only on the height of the liquid and not on the total amount of the liquid is called Pascal's second law. Although, to be fair historically speaking, a Flemish scientists Simon Stevin had already discovered this law over 50 years earlier. But Stevin made the mistake of writing in Dutch, not in the scientific language of Latin, and he had some political views that were too progressive for his time. And so his writings were happily ignored for long enough that Pascal's name took root. It is likely that Pascal had never heard of him when he was doing his own experiments. To understand the Stevin-Pascal law better let's think about pressure for a moment. Suppose you're at a dance party with supermodel Gisele and NFL quarterback Tom Brady. Who would you rather have step on you, Tom or Gisele spinning on her stiletto heel? At first glance you might want to choose Gisele, who weighs only half of what Tom does. But there's more to the story: if you've ever tried to walk on grass wearing heels you know how hard it is because your heels always sink into the dirt. if you wear flats or wedges you don't sink in and that's true even if you're carrying a heavy backpack. Why is that? Well when you're wearing flats your weight is distributed over the whole area of your foot, whereas when you're wearing heels it's concentrated on a very small point. And this highlights the essence of pressure: pressure is force per area and a small force can exert a huge pressure if it is concentrated in a small area. So even though Tom weighs twice as much as Gisele, his weight is distributed over his entire sole, which has about 500 times more area than Gisele's pointy stiletto. So the pressure under his foot is 250 times less than under Gisele's. Tom might give you a bruised toe, but Gisele would pierce straight through your foot and send you to the emergency room! Fun fact: even an elephant exerts less pressure on the ground than Gisele's heel. Now we can see how our 1 liter of water, which weighs only a couple of pounds, can create such a high pressure. As we squeeze this body of water into a narrower and narrower shape, we are in effect creating a stiletto of water. So here's the sneaky question which you're all probably thinking right now: Why do we need to pour the water into a long thin straw? Why can't be poor the same water into a funnel? It seems like we still have the same weight pushing down on a small opening at the bottom, shouldn't we got the same result? That's certainly much easier to do than going to the top of Fine Hall tower! Well, let's try it and see! Here we have a cylindrical straight walled tube filled with water, and next to it we have a funnel filled to the same height, clearly containing more water. We see here that the weight of this water in the first tube is balanced by 50 grams on the other side of the scale, as expected. Now let's see how much mass is required to balance the water in the funnel... 50 grams the same as the straight wall tube! But wait... if the vessel contains 630 grams of water, but only 50 grams are required to support the water, what is supporting the rest of the water? To solve this apparent conundrum we need to understand one more thing about pressure inside fluids like liquids and gases. In our first example Gisele's weight is acting in the downward direction and thus she exerts a pressure against the floor, but not against the wall or the ceiling. But take a look at this... I'm filling this enclosed container with smoke by pulling up on the piston. Notice how when I push downwards on the piston the smoke flows horizontally into the spherical glass bulb. If I continue pushing straight down the smoke escapes out of all the holes in the glass, not just the ones on the bottom but even the ones on the side and on the top. This means that the smoke is pushing against all surfaces of the container, including the walls and the ceiling. If I increase the pressure by pushing down harder, the smoke escapes faster in all directions, which means the pressure increases everywhere inside the gas. This is Pascal first law - that if the pressure at one point in an enclosed fluid increases, the pressure throughout the entire fluid also increases, and the fluid pushes in all directions. Although we have demonstrated this with a gas, you can imagine that the same thing would happen if we fill the container with water, or anything else that flows. Now let's go back to our funnel and see if we can shed light on our conundrum. Now we know that if we poke holes in the sides of the funnel, water will squirt out diagonally down, which means the water is pushing on the funnel in that direction. But since there is no hole the funnel wall is preventing the water from flowing out by pushing back against it in the opposite direction. So we see that even though the funnel wall is slanted, it pushes up as well as sideways against the water, and this is precisely the extra support that we were looking for. So it turns out that the walls of the funnel are supporting the extra water and the stopper at the bottom is only supporting the column of water directly above it. Let's try to use this idea to explain what happened with the third glass vessel here. When filled to the same height it contains much less water than either of the first two, and yet when we measure the weight required to support the water we see that it also takes 50 grams! Namely the force required to support the water is greater than the actual weight of the water! Where is that additional downward force coming from? Well let's remember to apply Pascal's first law: the glass vessel contains a horizontal ceiling part to it. If we poke holes in it the water would squirt up which means the water is pushing up against this part of the vessel. And thus the vessel is actually pushing down on the water, causing the stopper to support more than just the weight of the water. Now I pose a challenge to you: here is a slanted tube filled to the same height with water. Notice how most of the water is not directly above the stopper, and yet it also requires 50 grams to balance the pressure at the bottom. Why do you think that is? I'll leave that as a puzzle for you to figure out. This experiment is similar to the one Pascal did when discovering his laws. Aside from bursting barrels, of what use are these laws? Pascal invented what he called the "machine for multiplying forces," which we now call the hydraulic press. Suppose you have a vessel of water well filled on all sides with two apertures, one with a hundred times larger area than the other. If a piston is fit perfectly into each of these apertures and a force is applied to the smaller one, a hundred times greater force is required to balance the other piston, since the pressure is the same throughout the liquid. In this hydraulic press the platform has 11 times the area of the piston. This means that the force I exert on the piston is amplified 11 times. And this lever gives me an additional factor of 4. So overall the force is amplified 44 times, enough for me to easily bend this aluminum bar. The same force-multiplying mechanism is used to lift heavy objects like car, and in brake systems for some vehicles Even biology has had to adapt to these laws of nature. Let's use our new insights to try and predict which land animal has the strongest heart, namely the heart with the thickest walls. Thick, muscular walls are needed to create a high blood pressure. Well, the elephant is the largest animal by weight and thus requires the largest heart to pump the huge amount of blood. However, we now know that the total amount of blood is not what determines its pressure. The right question to ask is not, "which animal is the heaviest?" But rather, "which animal is the tallest?" And the answer is: the giraffe! Whose blood pressure reaches a whopping five pounds per square inch, or, using the unit more commonly used for blood pressure, 250 millimeters mercury. For comparison, the blood pressure in elephants reaches only 180 millimeters mercury, and in humans it's a mere 120, less than half of the giraffe's. Such a high blood pressure is required to push the blood up the giraffes 7-foot long neck and oxygenate the brain. And in order to create this huge pressure the muscles in the giraffe's heart need to be three inches thick! That's as thick as my finger is long! For comparison, the elephant's heart is two inches thick and human heart is 1/8 inch thick. Giraffes are truly fascinating creatures, and how their unique anatomy has adapted to the laws of physics is a rich topic... for another video. Fluids are exerting pressures all around us in our everyday lives. What other implications and applications of Pascal's laws, natural or man-made, can you think of? I would love to hear your ideas; please share your thoughts in the comments.
