Fluid Mechanics

Density, Pressure, and Buoyancy

Density - are you dense? Probably. Density is how compact an object is, how close its molecules are to each other. In other words, density = mass/volume.

Weight density, another kind of density, is equal to weight/volume.

Pressure - are you under pressure? Good. Pressure makes diamonds. Either way, Pressure = force / area. It is the amount of force in a certain area.

Liquids have lots of pressure. When a scuba diver swims in the ocean, they have to deal with pressure from the water above them. They can't swim too deep, or they will be crushed by it. When people send rovers towards the bottom of the ocean floor, they have to deal with pressure as well. Too much pressure might break the delicate parts of the rover. 

Now that seems heavy. Imagine the Earth's crust - I wouldn't want to be you. It's not just the pressure from the oceans that its dealing with. It has to handle air pressure from above.

In liquids, pressure acts in all directions. You don't feel more pressure on one side of your foot and less on the other when you're swimming because liquid pressure is equally exerted in all directions.

An equation for this would be: pressure in a liquid = weight density x depth

Now remember, pressure has nothing to do with volume, it only depends on depth. 

Buoyancy - are you buoyant? I sure hope so. Buoyancy is the upward force water exerts on an object. It is opposite to gravity and the reason why lifting heavy objects is easier when those objects are submerged.

Buoyancy acts upward because of water pressure. Since there is more water pressure the deeper you go, there is more pressure on the bottom of an object than the top, hence why the force pushes up.

An object sinks when it weighs more than the buoyant force pushing it up. If its weight is equal to the buoyant force, the object stays at whatever level maintains this equality. An object floats when it weighs less than the buoyant force once it is completely submerged.

When an object is dropped in water, is displaces the same amount of water as its volume. Basically, the water rises or overflows with the same volume of water as the volume of the object dropped inside. Big brain moment. Sometimes I like to imagine what it was like in the ancient world, reading a newspaper scroll thing on scientific discoveries, back when people were still realizing this stuff. Just think of the headline: 'NEW SCIENTIFIC DISCOVERY: WHEN YOU DROP SOMETHING IN WATER, THE WATER RISES 🤯' Hehehe.

Archimedes' principle is that the buoyant force on an object is the same as the weight of water it displaces. Basically, a rock displacing 1 N is affected by a buoyant force of 1 N. But, if the rock displaces 1 N, it also has a volume of 1 N and is being affected by a buoyant force of 1 N. With this logic, why does the rock not float? Why doesn't everything float? Well, you forgot weight! Objects sink because they weigh more than the buoyant force, which is because of density.

Buoyant forces acting on objects do not increase as the objects sink, since the amount of water displaced by an object is constant despite the depth of where it is in the water.

Flotation

When I first saw this word, my brain went, "why is that spelled so weird. Like damn." You guys have to agree with me - that looks wrong. It looks incorrect. It looks... disgraceful. Ah well, it is how it is.

Flotation works by making sure the required amount of water is displaced before an object can sink too far into the water. This means, the wider and flatter you make that object, the more water it will displace before it sinks too far inside.

This also applies to air, not just water. It applies to liquids and gases, which are fluids.

Flotation also depends on the density of the liquid. Humans float very easily on the Dead Sea compared to the Atlantic Ocean because the Dead Sea is far more dense with its high salt concentration.

Even though liquids and gases are fluids, they are different states of matter. Gas molecules are far apart while liquid molecules are much closer together. Thus, gas molecules are less restricted. They spread out and put pressure on the walls of their container.

When density is increased, so is pressure. Density can be increased by either doubling the amount of gas molecules in a container or by halving the space in the container.

As long as the temperature does not change, Boyle's law states, P1V1 = P2V2 where P1 and V1 are the original pressure and volume and P2V2 are the new pressure and volume. This law applies to ideal gases, where the effects of the forces between the molecules and the size of each molecule can be ignored.

Atmospheric Pressure

Atmospheric pressure is the weight of the air on a planet's surface. We don't notice it because we're submerged in it, the pressure in our bodies is equal to that of the surrounding air. We are well adapted to it, despite its crushing weight.

Now, air is heavy. 1 m^3 of air at sea level and at 20 degrees C has a mass of around 1.2 kg. If you don't think it's heavy, look up the weight of air needed to pressurize a 747 Jumbo Jet and reconsider.

Water has a constant density at any level, but air does not (assuming the water is at a constant temperature). As you gain altitude, air loses its density. Air pressure is also not constant or uniform across earth. Differences in air pressure are what meteorologists use to help predict the weather.

An example of how air pressure works is straws. When we drink from a straw, we suck the air into our mouths, reducing air pressure in the straw. Then, atmospheric pressure pushes the liquid up the straw. In other words, straws would be useless on Mars. Take the L.

Archimedes' principle applies to gases as well as liquids. We know that gases have a mass of 1.2 kg at sea level. That means, if we make a giant metal 1 m^3 cube, it displaces 1.2 kg of air. 1.2 kg of air is about 12 N, so the cube is pushed up with 12 N of force. If the mass of the object is less than 1.2 kg, it will float. if it is greater, it will sink.

Because air pressure changes with altitude, the amount of air displaced is different at different altitudes (this isn't english, I can start my sentences with "because" if I want to). Thus, a balloon will rise only until it can displace air that is equal to its weight. However, most balloons end up popping as they go higher - the air inside them expands and expands because of the pressure, making the balloon pop.

Breaking Physics With Water

I had no ideas for the title of this section 😭

A change in pressure on one part of a fluid is actually transmitted to every part. This property is called Pascal's principle, and it is really epic if I do say so myself. For example, in a hydraulic lift, a small force on the left side of the U shaped tube can lift a car on the right side. The pressure from the left side is exerted uniformly everywhere on the right side, lifting up the car with many times the force. This principle applies to all fluids.

This seems too good to be true. Where's the catch? Ain't no way we just broke physics. If we somehow assume that the car weighs 100 N and we push on the left side with 1 N of force, we multiply the force by 100. Co cool! But, if the water is pushed down 1 m, the car will be pushed up 100th of that meter, or one centimeter. Never mind guys, this trick is clearly only gonna work for a geezer with a lawnmower 💀

Bernoulli's Principle and Spinning Objects

Bernoulli's principle is the last thing we will discuss. It states that when a fluid's speed increases, the pressure inside of it decreases, and vice versa. Basically, as water flows from a larger pipe to a smaller one, it gets faster. However, its internal pressure is decreased. But remember - internal and external pressure are different. External pressure is the pressure a fluid exerts on its surroundings. Internal pressure is the pressure within the fluid.

Okay, last fact: when something spins, it curves because of how it interacts with the air around it. When a tennis ball spins, a layer of air is moved around the ball by friction. It produces higher pressure on one side of the ball, which curves it. That's pretty cool!

Either way, I hope you enjoyed this page! I hope to see you in Thermodynamics and Heat Transfer.