These 2 Videos Will Help You Understand Gauge Pressure and Archimedes' Principle

Photo Credit: Public Domain

By Andrew Bennett

What Is Absolute Pressure?

Absolute pressure is the force applied per unit of area (see my previous post on pressure).

What Is Gauge Pressure?

The pressure in a fluid is caused by the particles in the fluid colliding. As long as there is fluid present, there is pressure. So, why does my gauge read zero pressure when I have a flat tire?  Is there a perfect vacuum inside my tire?

We often measure what is known as "gauge pressure" (rather than absolute pressure), which simply subtracts atmospheric pressure from absolute pressure. Frequently, what we care about is actually the difference in pressure between what is in a container and what is outside the container (often atmospheric pressure), so gauge pressure is a convenient measurement. When the gauge reads zero, it simply means that the pressure inside the tire is equal to the pressure outside the tire, which is very close to "atmospheric pressure."

Gauge Pressure in a Sinking Submarine

If you were to get into a submarine at the water's surface, seal the submarine, and start sinking deeper into the water, you would be very interested in the difference in pressure between the air inside the sub (initially, this would be equal to atmospheric pressure) and the water outside the sub. You likely already know that the pressure grows as you get deeper in the water. Again, it isn't really the pressure outside the sub that presents a problem; it's the difference in pressure, so gauge pressure is still a useful quantity. As you go deeper, that difference in pressure would grow. (As a side note, this pressure difference would become too great for the submarine to remain intact when it went very deep, so it releases extra air on the inside as it goes deeper to increase the pressure on the inside.) In the video below, we'll look at why that happens and how to calculate the change in pressure related to depth.

Physics Video: Absolute vs. Gauge Pressure 

Even when we don't have water or another fluid in a vertical column, the same relationship applies.  Even in something like a curved pipe filled with water, the pressure will be larger at lower parts of the pipe. Parts of the pipe at equal depths (no matter how far removed horizontally) will also have equal pressures. The video below goes over this in more detail and walks you through some example problems.

If viewing via email, click here to see the video.

Upward Forces in a Fluid 

Objects placed in a fluid experience an upward force from that fluid. Sometimes, this force is large enough to make them float; sometimes, it isn't. Regardless, the upward force is an artifact of the difference in pressure depending on the depth of the fluid.  The bottom part of an object feels more pressure (and therefore more upward force) than the top of part an object, which feels less pressure (and therefore less downward force).

In the video below, we use a simple cube shape for an object in water to derive an expression for the magnitude of the upward force caused by the fluid surrounding the cube. The results of this line of thinking can be generalized to all shapes of objects in a fluid.

What Is Archimedes' Principle?

Archimedes' Principle is a generalized expression of these results. The principle states that any object surrounded by a fluid will experience a buoyant force equal in magnitude to the weight of the fluid displaced by that object.

An easy way to imagine this is to think of placing a cube underwater. Before that cube was in that location, there was water there. If we imagine a cube-shaped bit of water at that location, we picture it just sitting in place. To think that this cube of water would be falling through the rest of the water or floating up from the bottom doesn't make any sense unless we have the odd situation of the cube-shaped bit of water having a different density than the surrounding water.

What Is Buoyant Force?

Assuming that we have roughly uniform water, this cube-shaped bit of water should be in equilibrium. This means that the upward buoyant force on this water caused by the surrounding water must be exactly the same as the downward gravitational force on that cube of water. Replacing the cube of water with, for example, a cube of aluminum of the same size will have no impact on the buoyant force caused by the surrounding fluid. The force of gravity will change, but the buoyant force will not. The buoyant force will be equal to the weight of the cube of water that used to occupy that space.

The video below also includes a calculation of density for an unknown material using the properties of buoyancy on this object.

Note: There is a miscalculated value at the end of the video. I had an extra zero in the value of density, which should be 9,270 kg per cubic meter. There are little pop-ups about this in the video, but they don't display when you watch on the mobile version.

If viewing via email, click here to see the video.

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