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# Pressure in Fluids

by Ron Kurtus (revised 13 March 2016)

Pressure is a measurement of the force per unit area. * Fluid pressure* can be caused by gravity, acceleration, or forces in a closed container.

Since a fluid has no definite shape, its pressure applies in all directions. Fluid pressure can also be amplified through hydraulic mechanisms and changes with the velocity of the fluid.

Questions you may have include:

- How does gravity cause fluid pressure?
- How does air and water pressure apply in all directions?
- What are other applications of fluid pressure?

This lesson will answer those questions. Useful tool: Units Conversion

## Fluid pressure from gravity or acceleration

The weight of a fluid can exert a pressure on anything underneath it. Also, the relative movement of a liquid or gas can apply a pressure.

### Pressure

Pressure is defined as force divided by the area on which the force is pushing. (*See the lesson on Pressure for details.*) You can write this as an equation, if you wanted to make some calculations:

P = F/A

where

**P =**pressure**F**= force**A**= area**F/A**=**F**divided by**A**

### Pressure due to gravity

Since the weight of an object or material is equal to the force it excerts due to gravity,

An object can exert downward pressure due to its weight and the force of gravity. The pressure you exert on the floor is your weight divided by the area of the soles of your shoes. If the force is due to the weight (**W**) of the object, the equation is then: **P = W / A**

### Water pressure

The water pressure at the bottom of a lake is equal to the weight of the column of water above divided by the area of that column.

Pressure at depth is Weight / Area

#### Column on top of head

If you were standing on the bottom of a swimming pool (assuming you would not start floating), there would be a column of water the diameter of your head all the way up to the water surface, pushing down on you. If you took that column of water and weighed it, and then divided that weight by the area of the top of your head, you would get the value for the water pressure on your head.

The reason it does not affect you is that your internal body pressure increases to neutralize most of the water pressure. But at greater depths, the water pressure can become so great that it can harm the diver.

#### Demonstration with can

A demonstration of how water pressure increases with the depth of the water can be done with a large tin can. Punch nail holes in a vertical line up the side of the can every inch or several centimeters. Then fill the can with water. The water may just dribble out the top holes, but the increased pressure with depth causes the water to squirt out with more pressure at the bottom holes.

### Air pressure

Likewise, the air pressure on the top of your head is the weight of the column of air (which is several miles high) divided by the area of the top of your head. The average air pressure on your head is 14.7 pounds per square inch! That is a lot of weight you are holding up.

#### Air pressure in weather

When weather report indicates high pressure, that means the column of air reaches up higher than it does for a low pressure reader. A barometer measures the air pressure or the weight of the column of air.

Air pressure is due to the weight of all the air going several miles up above you. It is approximately 16 pounds per square inch in all directions on your body. Fortunately, our bodies have internal pressure that equalizes the air pressure.

#### Balloons

The air pressure inside a balloon pushes outward in all directions. When the pressure increases, the size of the balloon increases, until it finally bursts. The internal air pressure is much greater than the external air pressure.

#### Different altitudes

The normal air pressure in Denver, Colorado is less than in This is because the higher altitude of Denver means its column of air is not as high as in Milwaukee.

Since many snacks are sealed in pressurized bags, a bag sealed in Milwaukee requires higher internal pressure than one made in Denver. Thus a Milwaukee bag of snacks will expand when brought to the lower air pressure of Denver and could even explode.

## Direction of fluid pressure

Now, what is different about pressure caused by a liquid, or gas is that not only is there pressure pushing down at a given point, but there is also the same pressure pushing up and to the sides.

### All directions

The pressure is the same in all directions in a fluid at a given point. This is true because of the characteristic of liquids and gases to take the shape of their container.

Water pressure is the same in all directions

What this also means that any hollow container submersed in a liquid has pressure on every square inch of its surface, top and bottom.

### Swimming under water

When you swim under water, the pressure of the water gets greater on your body, the deeper you get. Now, the question is: "Why aren't you crushed by all this weight?"

The reason is that your body compensates by creating an internal pressure that is equal to the air or water pressure. You are somewhat like a balloon filled with fluids under pressure. Now, when you go very deep under water, the water pressure may get greater than your body can compensate for, and you get uncomfortable.

## Other pressure effects

Other effects of fluid pressure are motion, heating and chemical effects, as well as applications in the field of hydraulics and in aircraft.

(

See Applications of Fluid Principles for details.)

### Wind and current

The movement of a fluid, such as with wind or the current of a river can apply a pressure to an object in its way proportional to the surface area perpendicular to the direction of motion.

Streamlining the object reduces this pressure.

### Heating and chemical effects

When you heat a fluid, it usually expands. If you heat a fluid that is in an enclosed container, the expansion will result in greater internal pressure. For example, heating a balloon will cause it to expand.

Likewise, chemical reactions that give off gases will increase the pressure inside the container. For example, shaking a carbonated drink bottle releases more gas and will result in greater internal pressure. This can be experienced when you open the bottle and the drink squirts all over.

### Hydraulics

When a fluid—especially a liquid—is in a partially closed container, a force applied in one area can result in a greater force in another area. This effect is used in hydraulics to create a mechanical advantage by having the force applied to a small piston resulting in a greater force applied to large piston.

### Aircraft

The scientist Bernoulli discovered that the air pressure in a tube goes down when the velocity of the air in the tube increases. This discovery became known as *Bernoulli's Principle*.

The greatest application of this principle is used in airplanes. The wing of an airplane is usually curved on top and flat on the bottom. When the air moves over the curved top portion of the wing, it speeds up because of the shape. This lowers the pressure with respect to the bottom part of the wing. Lower pressure on the top results in the lift required to keep the airplane aloft.

## Summary

Fluid pressure from gravity is the weight of the fluid above divided by the area it is pushing on. Fluid pressure applies in all directions. Internal pressure of an object equals the external fluid pressure, otherwise the object could be crushed. Wind and heating can also create pressure.

Be able to perform under pressure

## Resources and references

### Websites

### Books

**Top-rated books on Physics of Fluids**

**Fluid Mechanics** by Ira M. Cohen and Pijush K. Kundu, Academic Press (2004) $74.95

**Vectors, Tensors and the Basic Equations of Fluid Mechanics** by Rutherford Aris, Dover Publications (1990) $14.95

**Fundamentals of Fluid Mechanics** by Bruce R. Munson, Donald F. Young, Theodore H. Okiishi; Wiley (2001) $37.95

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## Pressure in Fluids