# Hydrostatic Pressure: Definition, Equation, and Calculations

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• 0:01 Pressure
• 0:59 Pressure in a Liquid
• 2:25 Calculating Liquid Pressure
• 3:46 Examples
• 6:11 Lesson Summary
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Instructor
Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Expert Contributor
Kathryn Boddie

Kathryn earned her Ph.D. in Mathematics from UW-Milwaukee in 2019. She has over 10 years of teaching experience at high school and university level.

This video lesson will introduce you to hydrostatic pressure in a liquid, as well as provide examples for how to calculate the liquid's pressure at a given depth.

## Pressure

When you step on a scale, you get a reading of your weight, which is simply the force due to gravity. Your weight on the scale will read the same no matter how you stand on it - with both feet on the scale, with one foot in the air or even if you do a handstand!

What's different is the pressure you exert on the scale in each of these situations because this is the force exerted over a given area, or in equation form, P = F/A. Your weight is the force, but the pressure depends on how much area that weight is applied over, be it both feet, one foot or your two hands.

Pressure in a liquid is also the force exerted over a given area, but the difference is that a fluid's pressure pushes on the walls of the surrounding container, as well as on all parts of the fluid itself. This is true for both liquids and gases because they are both fluids, but pressure in a liquid is a little different from that of a gas.

## Pressure in a Liquid

Gas particles are not very friendly. They spread out to fill the entire space of their container, enjoying their personal space and freedom. But as gas particles fly around, they sometimes collide with each other, as well as the walls of the container. These interactions create pressure in the container, and in a gas, this pressure is the same throughout the entire fluid.

But you can clearly see that this is not the case for liquids because they do not fill their entire container like gases do. This is because of the bonds between the liquid's molecules, which are what hold them together. When you pour a liquid into a container, it fills the bottom because gravity pulls it down. This force due to gravity is the same as your scale reading - it's the liquid's weight and is what creates pressure in that liquid.

The pressure in the liquid also increases with depth because of gravity. The liquid at the bottom has to bear the weight of all the liquid above it, as well as all of the air above that! You don't notice the weight of the air around you because your body is 'pressurized' the same as the atmosphere, but any liquid under that atmosphere definitely feels it.

You can experience this change in pressure when you swim to the bottom of a pool. As you go deeper underwater, you feel the pressure increasing because there is more and more weight on top of you. But the pressure doesn't just build up on top of you. Because you're in a fluid, you'll feel that pressure increase all around you.

## Calculating Liquid Pressure

When a liquid is at rest, meaning that it is not flowing, we can determine its pressure at a given depth known as hydrostatic pressure. The way we determine this is through an equation: P = rho * g * d, where P is the pressure, rho is the density of the liquid, g is gravity and d is the depth.

You may also see the hydrostatic equation written as P = rho * g * h, where the h stands for height. This may be used because sometimes we want to calculate the pressure of a liquid as it fills a column (like when measuring barometric pressure), so we need to know the height of the fluid. It's like taking the depth and flipping it upside down. As long as you use the appropriate measurement, either letter is okay to use, but it might help to stick with the letter that best represents what you're measuring - either the depth or the height.

It's important to remember that the density of the liquid doesn't change with depth any more than the density of a candy bar changes when you break it into separate pieces. Liquids are not compressible, meaning their molecules are already about as close together as they can be. It's also a good time to take note of that g in the equation. It acts as a constant reminder of how gravity plays a crucial role in the pressure of a liquid at any given depth.

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## Comparing Hydrostatic Pressure in Different Liquids

In the following examples, students will calculate the hydrostatic pressure of a liquid at a certain depth, given the liquid's density. Students will also get practice finding the depth of the liquid, given the density and the hydrostatic pressure as well as practice finding the density of the liquid, given the depth and the hydrostatic pressure. After completing these beginning examples, students will be more comfortable manipulating the equation for hydrostatic pressure to solve for different variables. Then students can move on to the challenge example, where they will solve to find what depth for different liquids are needed so that the liquids have the same hydrostatic pressure.

## Beginning Examples

• Find the hydrostatic pressure of water at the bottom of a 7 meter pool. The density of water is 1000 kg/m^3.
• At what depth is the hydrostatic pressure of gasoline equal to 50,000 Pa? The density of gasoline is 725 kg/m^3.
• What is the density of diesel, given that the hydrostatic pressure at a depth of 4 meters is 33,712 Pa?

## Solutions

• We will use the formula P = rho * g * d where rho is the density of the liquid, g is gravity, and d is the depth of the liquid. We have P = 1000 * 9.8 * 7 = 68,600 Pa for the hydrostatic pressure of water at the bottom of a 7 meter pool.
• Using the same formula P = rho*g*d, we have 50,000 = 725 * 9.8 * d, and so we have 50,000 / 7105 = d. The depth is about 7.04 meters.
• Using the same formula P = rho * g * d, we have 33,712 = rho * 9.8 * 4 and so we have 33,712 / 39.2 = rho. The density of diesel is 860 kg/m^3.

## Challenge Problem

• At what depth is the hydrostatic pressure for gasoline equal to the hydrostatic pressure for water at the bottom of a 10 meter pool? Remember that the density of water is 1000 kg/m^3 and the density of gasoline is 725 kg/m^3.

## Solution

• First, find the hydrostatic pressure of the water at a depth of 10 meters. We have P = 1000 * 9.8 * 10 = 98,000 Pa. We now need to find what depth is needed for the hydrostatic pressure of gasoline to also equal 98,000 Pa. Using the formula again, we have 98,000 = 725 * 9.8 * d and so 98,000 / 7105 = d. The depth is about 13.79 meters. This means that if you are submerged 13.79 meters in gasoline, the pressure will feel the same as the pressure of being submerged 10 meters in water.

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