PhET Under Pressure Simulation
Measure the pressure in a fluid and how it changes with depth, density of the liquid, and gravity. You can also try different container shapes to see what effect it has on pressure.
Hello there! Welcome to lecture 13: liquids!
A liquid is a material where the molecules or atoms are free to move about much easier than in a solid, however the molecules are still packed rather close together. A liquid will change its shape, but cannot be easily compressed to change its volume.
Liquids play a huge and important role in our lives. This video will explain many important properties about liquids, and will help you to understand why things float, the basic idea of how water systems work, and more!
Each of the following concepts will be discussed in this video: pressure, Archimedes’ principle, flotation, pascals principle, surface tension, and capillarity.
Pressure is a concept that is important in solids, liquids, and gases. We’ll discuss atmospheric pressure in lecture fourteen. For now, let’s talk about pressure caused by solid and liquid objects.
The symbol for pressure is the capital letter P. The SI units of pressure are pascals, which can be broken down into units of newtons divided by meters-squared. Pressure caused by a solid object is equal to force divided by area, or P equals F divided by A. In other words, this is the amount of force divided by the amount of area over which the force is applied.
When I participated in the “bed of nails” demo, which was explained in lecture seven, the reason the nails don’t hurt me too much when I lie down on them is because the weight of my body, the force involved in the equation, is distributed over a large number of nails. While each nail has a relatively small surface area, the combined surface area of all of the nails causes the pressure to be smaller. I would not have done this demo if there had only been one nail on the board!
Pressure is also a concept that is important in fluids: liquids and gases. In a liquid, the pressure is equal to the density of the liquid times the gravitational acceleration times the depth. Another equivalent way to write this equation would be to say that P equals m divided by V (which is the equation we use for density) times g, times depth.
If you’ve ever gone swimming or scuba diving and had your ears pop, that’s because the pressure in water increases as you swim deeper and deeper. Note that the equation for pressure does not have to do with how large an area the liquid is distributed over: it only has to do with the density, gravitational acceleration, and depth. If you dive 5 meters under the surface of Lake Michigan, you would experience the same pressure that you would 5 meters under a freshwater pond, even though the two bodies of water are different sizes.
One of the consequences of liquid pressure is that water always seeks its own level in a container. If you’ve ever taken a container of liquid and tilted it, perhaps you’ve noticed that the water level will always even out.
If we look at an animation of a container of liquid, as it gets tilted, the height of the water is unequal from one end to the other. In this case, the left-hand side has a higher height above the bottom of the container, and the right-hand side has a lower height above the bottom. This causes more pressure to be present on the left. If there’s more pressure, there’s going to be a net force between left and right side. Newton’s laws tell us that when there’s a net force, there will be an acceleration. The water will move until the height is equal on both sides, causing an equal amount of pressure and no net force.
If you’ve gone swimming, you may have noticed that you feel like you weigh less in water than you do on land. It’s true! Liquids exert an upward buoyant force on us, which means we exert less of a support force if we’re standing in a pool or other shallow body of water. If the density of the water is high enough, such as in salt water, the buoyant force may actually cause us to float!
The buoyant force acting on an object placed in a liquid has to do with the differences in that fluid pressure. For example, a cube placed in water is going to have pressure exerted on each of the faces of that cube, creating a force on each cube face. Because pressure increases with depth, the lowest part of the cube has more force than the highest part of the cube. All of the horizontal forces on the cube cancel out. The net force is a force pointing upward. This is the buoyant force!
All objects placed in water have a buoyant force pointing upward. If I place an object that sinks at the bottom of a container filled with water, that buoyant force will act on the object. When the object sinks, it stays put at the bottom of the container. There’s no net force. This means the gravitational force acting on the object (mass times gravitational acceleration) is cancelled out by the buoyant force and support force. The buoyant force causes the support force to decrease. This is why we feel lighter in a swimming pool.
An object that floats will have a buoyant force greater than or equal to the gravitational force acting on the object. If I submerge the floating object in water, the buoyant force, being greater than gravitational force, leads to a net force, causing the object to accelerate upward. At some point the object will reach equilibrium as it rests on the surface of the water. The buoyant force decreases as the object displaces less liquid as it moves upward out of the water. When the gravitational and buoyant forces are equal, the object will stop moving and simply float.
Archimedes’ principle states that the buoyant force is equal to the weight of the fluid that is displaced when a solid object is placed into a fluid. This means that the buoyant force is equal to the density of the fluid, the volume that is displaced, times the gravitational acceleration. Remember what units we use for force? That’s right, newtons! Recall that newtons are a kilogram times meter divided by second-squared. Let’s see what units our terms have to be in to get a buoyant force in units of newtons. The density will have to be measured in kilograms per meter-cubed, the volume displaced will have to be measured in meters-cubed. As we know, gravitational acceleration has units of meters per second-squared. If we have different units for density or volume, then we must do a unit conversion before determining the force in newtons.
A second equation we can use to quantify buoyant force is that the buoyant force on an object is equal to the weight of the object in air minus the weight of the object in the fluid.
I have here two spheres, one is iron and one is wood. They both have the same size and shape, which means they have equal volumes. Which one will have a larger buoyant force when I place them into a fish tank? Let’s find out!
The weight of the iron sphere is 17.9 newtons when measured in air. The weight of the wood sphere is 2 newtons when measured in air. When I place both objects into the fish tank, the iron sphere sinks to the bottom of the tank, and the wood sphere floats. Measuring the weight in the water, the weight of the iron sphere is now 15.5 newtons, and the weight of the wood sphere is zero newtons. It makes sense that the wood sphere is now weightless because it is floating!
Using the equation for buoyant force, we see that the buoyant force acting on the iron sphere is 17.9 minus 15.5 newtons, or 2.4 newtons. The buoyant force acting on the wood sphere is 2 newtons. There is more buoyant force acting on the iron sphere than the wood sphere.
Archimedes’ principle also backs this up. Remember that the buoyant force is equal to the weight of the displaced water. Which of these spheres displaces more water? The iron or the wood? Think about it!
Here’s another interesting demo of Archimedes’ principle. I have a heavy brass ball sitting on some dried beans. When I shake the container, the brass ball moves downward to the bottom of the container, and out pops a ping-pong ball! The ping-pong ball has a lower density than the dried beans, and therefore experiences a buoyant force. The brass ball has a high density and sinks. This only works when I shake the container, creating a type of fluid flow.
In lecture 14, we’ll talk about how Archimedes’ principle also applies to gases. Remember, gases are a fluid too!
The principle of flotation states that any object that floats displaces a weight of fluid equal to its own weight. Notice that this is similar to Archimedes’ principle, except its stated in terms of weight rather than volume. A boat that has a weight of 10,000 Newtons will float if it displaces 10,000 Newtons of water.
A solid piece of iron has a density approximately 8 times greater than that of water. This means that if we were to place a piece of solid iron into a container of water, it would only displace one eighth of its weight in water. This is not enough to make it float.
If iron sinks in water, how is it that boats and submarines can be made out of iron and other dense metals? If you think about the shape of a boat in a simplistic manner, it is carved out so that it is able to displace its own weight in water. Effectively, the boat has sections of air that cause the overall density to be less than that of the fluid its floating on.
An object that is less dense than a fluid will float in that fluid. An object that is more dense than a fluid will sink in that fluid.
You will explore the principle of flotation in the lab on Archimedes’ principle.
Pascal’s principle states that a pressure change everywhere in a closed system of a liquid is equal.
Here I have a system consisting of two pistons with water in between. When I press down on one side, it causes a pressure change that transmits throughout the liquid, causing the second piston to rise up.
Pressure, force and area are related. If I exert one newton of force over one square centimeter, then one newton per square-centimeter will be transmitted to the second piston. If that second piston has an area of 2 square-centimeters, then it can now support a weight of two newtons, twice the force that I exerted!
In equation form, Pascal’s principle can be stated that delta F one divided by A one equals delta F two divided by A two. In other words: the change in force divided by the area at one point in a system equals to the change in force divided by area somewhere else in the system.
This forms the basis of hydraulic systems. I can exert a small force on a small area and achieve a large force output on a large area somewhere else.
I can lift a mass of 500 grams using a smaller mass of 200 grams. Because of differing amounts of area, I amplified the force by a factor of two and a half!
If I were to make this second area much, much larger, maybe you could see how it could be used to lift something really large, like a car. Hydraulic lifters use this principle to lift heavy objects. Hydraulics are also used in automobile braking systems. Exerting a small force on a pedal causes our cars to slow down. Hydraulics are also used in large airplanes. Pilots can exert a small force on a control yoke or rudder pedals and a hydraulic system creates a deflection in the airplane flight controls that would otherwise be too heavy for humans to move on their own.
Pascal’s principle also forms the foundation for modern water supplies and distribution systems. In the Midwest where it’s relatively flat, we have water towers to create water pressure. When I open the tap on my sink, I have good water pressure because my house is connected to a water main that’s pressurized.
The bad news is, that if the water main breaks, then water pressure will be lost everywhere in the water system! When I lived in Boston, there was a water main break in 2010 that caused about two million people, including myself, to have no water pressure in our homes and apartments. Because the pressure change is transmitted throughout a system, a water break in one spot will transmit everywhere!
Surface tension is a force that acts parallel to a surface of liquid, such as water.
In a volume of water, bonds between molecules will cause the molecules in the center of the water to have no net force. Molecules at the surface don’t have forces acting on them in all directions, causing a force of surface tension.
In most liquids, including water, surface tension causes water to form drops. The spherical shape of the drop minimizes the amount of force present on the surface. In a way, you can think of the spherical shape as the most comfortable arrangement for the molecules.
Surface tension also explains how objects with enough surface area can rest on the top of water without getting submerged.
This paperclip is not floating – aluminum is more dense than water, so we would expect it to sink. However, the paperclip is sitting on top of the water due to the surface tension of the water being greater than the weight of the paperclip. If I push on the paperclip, I increase the downward force enough to break through the surface tension. The paperclip then sinks, as predicted by the principle of flotation.
This is how insects like water striders walk across water. It also explains why it hurts to do belly flops into a swimming pool!
Capillarity is related to surface tension. When liquids are in a narrow space, they can cause a meniscus or, if in a narrow enough space, rise up the walls of a container. The adhesive force between water and glass is greater than water’s cohesive force. In other words, water would rather situate itself to be next to glass molecules than next to other water molecules. This arrangement, creating a meniscus shape, minimizes the forces in the water.
Capillarity explains how paper towels absorb moisture, how trees get water from their roots to their branches, and how small amounts of blood can be drawn using a finger stick.
Note that this does not work with all liquids. Any liquid with more cohesive forces than adhesive forces will form a convex meniscus, which is the opposite shape that we see with water. Mercury is an example of a liquid that is very cohesive, meaning that capillarity would not work with mercury.
Thanks for taking the time to learn about liquids. Until next time, stay well.