Water pressure and density relationship

How does pressure affect density of fluid?

water pressure and density relationship

The pressure exerted by a static fluid depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravity. The pressure in a static fluid Discussion. Fluid column height in the relationship inches water= cm water. Density is related to volume by the fact that density is defined as mass divided by volume: [math]\displaystyle \rho ={\frac {m}{V}}[/math] So a relationship between. as the depth increases, wouldn't the density of the liquid increase because of the This table gives the compressibility of some liquids, including water. However when applying a physics relation it is important to understand.

water pressure and density relationship

The force down is going to be equal to the mass of the liquid times gravity. What is that mass of the liquid? 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.

What is pressure?

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?

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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.

water pressure and density relationship

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. 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?

water pressure and density relationship

The volume of the liquid is going to be the cross-sectional area of the cylinder times the height. So let's call this cross-sectional area A.

Pressure and Density - A level Physics

A for area-- that's the area of the cylinder or the foil that's floating within the water. We could write down that the downward force is equal to the density of the fluid-- I'll stop writing the l or f, or whatever I was doing there-- times the volume of the liquid.

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The volume of the liquid is just the height times the area of the liquid. So that is just times the height times the area and then times gravity.

We've now figured out if we knew the density, this height, the cross-sectional area, and the gravitational constant, we would know the force coming down. That's kind of vaguely interesting, but let's try to figure out what the pressure is, because that's what started this whole discussion. What is the pressure when you go to deep parts of the ocean? This is the force-- what is the pressure on this foil that I have floating?

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It's the force divided by the area of pressure on this foil. So I would take the force and divide it by the area, which is the same thing as A, so let's do that.

Let's divide both sides of this equation by area, so the pressure coming down-- so that's P sub d. The downward pressure at that point is going to be equal to-- keep in mind, that's going to be the same thing as the upward pressure, because the upward force is the same. The area of whether you're going upwards or downwards is going to be the same thing.

The downward pressure is going to be equal to the downward force divided by area, which is going to be equal to this expression divided by area. Essentially, we can just get rid of the area here, so it equals PhAg divided by A-- we get rid of the A's in both situations-- so the downward pressure is equal to the density of the fluid, times the depth of the fluid, or the height of the fluid above it, times the gravitational constant Phg.

As I said, the downward pressure is equal to the upward pressure-- how do we know that? Because we knew that the upward force is the same as the downward force. Scales are often employed to determine the mass of a substance since weight is a function of mass and gravity.

Since gravity is very nearly the same over the surface of the Earth, weight becomes a good indicator of mass.

water pressure and density relationship

Increasing and decreasing the amount of material measured increases and decreases the mass of the substance. Volume Volume describes how much space a substance occupies and is given in liters SI or gallons English.

The volume of a substance is determined by how much material is present and how closely the particles of the material are packed together. As a result, temperature and pressure can greatly affect the volume of a substance, especially gases.

As with mass, increasing and decreasing the amount of material also increases and decreases the volume of the substance. For example, 10 grams of freshwater has a volume of 10 milliliters.

water pressure and density relationship

Unlike mass and volume, increasing the amount of material measured does not increase or decrease density. This makes density a useful property in identifying many substances.

However, since volume deviates with changes in temperature and pressure, density can also change with temperature and pressure. Specific Gravity One derivative measurement of density is specific gravity. Specific gravity compares the density of a substance with the density of a reference material. In the case of gases, the reference material is standard dry air, or air without water.

In the case of liquids and solids, the reference material is fresh water. Specific gravity is calculated by dividing the density of a substance by the reference substance's density. For example, gold has a density of