# Pressure and density relationship liquid

Density and pressure have an integral relationship. The higher the density of This is especially true for liquids and gases. Density. Density is. Pressure within a liquid depends only on the density of the liquid, the acceleration due to Equation 2 by itself gives the pressure exerted by a liquid relative to. Density and specific volume of a liquid versus change in pressure and temperature.

At this point, if you've been paying close attention you might wonder "Hey, there's air above the water right? Shouldn't the weight of the column of air above the column of water also contribute to the total pressure at the top of the can of beans?

- Static Fluid Pressure
- What is pressure?

The air above the column of water is also pushing down and its weight is surprisingly large. The force from atmospheric pressure on the top of a chessboard would be comparable to the weight of a car. You might wonder how we can pick up the chessboard so easily if the weight of a car is pushing down on it, but it's because the weight of a car is also pushing up on it.

Remember that the force from fluid pressure does not just push down, it pushes inwards perpendicular to the surface from every direction. It may not seem like there is any air under the chessboard when placed on the table but the roughness and cracks of the chess board are enough to allow air underneath.

If you could get rid of all the air underneath the chessboard and prevent air from being allowed to sneak back in, that board would be stuck to the table like a suction cup. In fact, that's how suction cups work. They push the air out to create less pressure inside than out. We'll see later that the atmosphere actually adds pressure on top of this.

### What is pressure? (article) | Fluids | Khan Academy

Let's assume that there's no air, but it's on a planet of the same mass, so the gravity is the same. There is gravity, so the liquid will fill this container on the bottom part of it. Also, the gravitational constant would be the same as Earth, so we can imagine this is a horrible situation where Earth has lost its magnetic field and the solar winds have gotten rid of Earth's atmosphere.

That's very negative, so we won't think about that, but anyway-- let's go back to the problem. Let's say within this cylinder, I have a thin piece of foil or something that takes up the entire cross-sectional area of the cylinder. I did that just because I want that to be an indicator of whether the fluid is moving up or down or not.

**Pressure at a depth in a fluid - Fluids - Physics - Khan Academy**

Let's say I have that in the fluid at some depth, h, and since the fluid is completely static-- nothing's moving-- that object that's floating right at that level, at a depth of h, will also be static.

In order for something to be static, where it's not moving-- what do we know about it? We know that the net forces on it must be zero-- in fact, that tells that it's not accelerating. Obviously, if something's not moving, it has a velocity of zero, and that's a constant velocity-- it's not accelerating in any direction, and so its net forces must be zero. This force down must be equal to the force up.

## Pressure at a depth in a fluid

So what is the force down acting on this cylinder? It's going to be the weight of the water above it, because we're in a gravitational environment, and so this water has some mass. Whatever that mass is, times the gravitational constant, will equal the force down. Let's figure out what that is. The force down, which is the same thing is the force up, is going to equal the mass of this water, times the gravitational constant.

Actually, I shouldn't say water-- let me change this, because I said that this is going to be some random liquid, and the mass is a liquid. The force down is going to be equal to the mass of the liquid times gravity. What is that mass of the liquid?

## Water Density

Well, now I'll introduce you to a concept called density, and I think you understand what density is-- it's how much there is of something in a given amount of volume, or how much mass per volume. That's the definition of density.

The letter people use for density is rho-- let me do that in a different color down here. The units are kilograms per meter cubed-- that is density. I think you might have an intuition that if I have a cubic meter of lead-- lead is more dense than marshmallows. Because of that, if I have a cubic meter of lead, it will have a lot more mass, and in a gravitational field, weigh a lot more than a cubic meter of marshmallows.

Of course, there's always that trick people say, what weighs more-- a pound of feathers, or a pound of lead? Those, obviously, weigh the same-- the key is the volume.

A cubic meter of lead is going to weigh a lot more than a cubic meter of feathers. Making sure that we now know what the density is, let's go back to what we were doing before. We said that the downward force is equal to the mass of the liquid times the gravitational force, and so what is the mass of the liquid? We could use this formula right here-- density is equal to mass times volume, so we could also say that mass is equal to density times volume. I just multiply both sides of this equation times volume.

### How does pressure affect density of fluid?

In this situation, force down is equal to-- let's substitute this with this. The mass of the liquid is equal to the density of the liquid times the volume of the liquid-- I could get rid of these l's-- times gravity. What's the volume of the liquid? The volume of the liquid is going to be the cross-sectional area of the cylinder times the height.