GRADES 1-8
AIR AND WATER PRESSURE

BACKGROUND INFORMATION: Fluid dynamics is the study of how gases and liquids behave. A fluid can be either a gas or a liquid. All substances have three states of matter: solid, liquid, and gas. When a substance is in a solid state, its molecules are all lined up and rigid. Its volume and shape are fixed. An ice cube (solid water) remains an ice cube no matter what size or shape a container you put it in. A liquid, on the other hand, has molecules that are more fluid and moveable. It has a fixed volume, but it can take the shape of its new container. You can pour a quantity of water from a glass to a cube, but if the cube has a smaller volume than the glass, the water will run over the top! A gas has molecules that are completely free to move about, contracting and expanding at will. A gas has no fixed volume or shape. If you take a deep breath of air (a gas), the air you take in expands to fill all the compartments of your lungs. If you blow that breath into a balloon, for instance, the volume in the balloon is much smaller than the volume in your lungs. We measure the number of molecules in a given volume of fluid and call it density. Since the volume of a liquid is constant, its density, the mass (measured by the number of molecules) in a fixed volume, is also constant. A liquid is considered to be incompressible; the density is constant and you can't squeeze more mass into the same volume. With a gas, you can continue to add molecules into a given volume, or you can squeeze the same number of molecules into a smaller volume. When you do this, the density changes and the gas is called a compressible fluid. A fluid exerts a pressure on the container holding it. Pressure is a series of small forces acting on all the surfaces the fluid touches. A force is a push; it is a vector, meaning it has both a magnitude (the amount) and a direction in which it is acting. Pressure is measured as the force per area. The pressure is not a vector because it exists in all directions. We can measure the pressure of a gas like air at sea level on a still day, and show that the pressure is constant and equal to 14.7 pounds per square inch (psi). This is called atmospheric pressure. An open, flat balloon has the same atmospheric air pressure on both the inside and the outside. When we blow into the balloon, however, we increase the pressure above atmospheric pressure. The increased pressure inside the balloon causes the sides of the balloon to bulge outward. In Activity 2, we used the increased air pressure in our balloon to raise the book off the table surface. In Activity 5, when we put the lid with the hole taped up on the tub, we took away the atmospheric pressure acting on the water in the tub. When we took the tape off the bottom hole, the atmospheric pressure acting on the bottom of the tub was much greater than the pressure inside the tub, so the water stayed in the tub! Even the weight of the water in the tub wasn't enough to overcome the pressure difference. Once the tape was removed from the top hole, however, the pressure on both the top surface and the bottom surface of the tub were equal, and the weight of the water forced it to run out the hole! When we analyze fluids in motion, we will often do our calculations for 'idealized' flows. This means we make assumptions about the flow to simplify our equations of fluid motion to algebraic equations. We can get a good idea of the fluid behavior for these idealized conditions. Usually, the negatives we are ignoring are small and don't affect the answer too much. When we can define our fluid flow along fixed lines (along a pipe, for example) and with no energy changes, we can use the Bernoulli equation. By energy changes we mean something that takes an effort, work, or chemical catalyst to change. For example, we talk about how things flow in nature: water runs downhill, not uphill. It takes energy, or some type effort, to go against nature. When we are following nature and not using any energy, we can use the Bernoulli equation to compute values in our flow. Daniel Bernoulli was a Swiss mathematician who lived in the early 1700's. He developed a series of mathematical expressions to explain basic fluid flow phenomena. He is most famous for developing an expression for idealized flows. In its most common form, the Bernoulli equation states that the local pressure plus the dynamic pressure (caused by the motion of the air) is equal to a constant. In Activity 1, we are using the Bernoulli principle to hold up the balloon or the ping pong ball. As you blow upwards around the ball, the air splits into multiple air streams around it. At the bottom of the ball, the velocity is actually 0; the velocity on the sides of the ball is increasing. Bernoulli's equation says that as the velocity increases, the local pressure decreases! Where there is no velocity the pressure is at its highest. So the pressure at the bottom of the ball is higher than the pressure on the sides, and the ball is held up by the airstream. Activity 4 demonstrates the Bernoulli equation also. When you blow into the spool, the air coming out the bottom moving over the card is at a fairly high velocity, so the local pressure on the top side of the card is lower than the atmospheric pressure pressing up from the bottom of the card, where there is no air moving. The pressure difference keeps the card in place! Buoyancy is the final concept we want to discuss here. When an object is immersed in a fluid, what makes it float? Archimedes' principle states that the fluid exerts an upward force on the object equal to the weight of the fluid that is displaced by the object. This means that if you have an object whose mass is less than that of the fluid, the fluid forces will push that object up! This is why a boat floats or a hot air balloon floats through the air. The weight of the boat (its mass times gravity) is less than the weight of the water it displaces. In Activity 3, the students built boats and placed pennies in them. As long as the boats displaced a large volume of water, multiple pennies could be placed in them. If the foil boats didn't displace much water, then they wouldn't be able to hold many pennies. The wadded up piece of foil didn't displace very much water at all, and the weight of the wad was greater than the weight of the water it displaced, so it sunk to the bottom. Hot air balloons also work on the buoyancy principle. As the air heats up, its density decreases. Once the balloon is expanded to its full size, its volume is fixed. As the density continues to decrease, that means the mass is decreasing. Since weight is the mass times gravity, the weight of the hot air is less than the weight of the cooler air it is displacing, and the balloon rises into the air!