# Fluid Mechanics

### pressure flow boat piston

Fluid mechanics is the study of gases and liquids at rest and in **motion**. Fluid statics studies the behavior of stationary fluids and tells us, for instance, how much air to put in our tires and whether a boat in a **lake** will float or sink. **Fluid dynamics** studies the flow behavior of moving fluids. Both global **weather** patterns and the flow of **water** from a faucet are governed by the laws of fluid dynamics.

A fluid at rest exerts static **pressure** on its container and on anything that is submerged in it. The pressure at any point in the fluid is the **force** that would be exerted on unit area of a submerged object. This pressure is the same in all directions. Because of gravity, the pressure in a fluid increases as one goes deeper below the surface. Marine creatures dwelling deep down in the **ocean** have to withstand greater pressures, due to the weight of the water above, than **fish** swimming near the surface. The exact pressure at different depths depends only the **density** of the fluid and the depth from the surface.

This pressure increase with depth also provides the upward buoyant force on a floating object. The pressure below a boat is greater than the pressure at higher points and, therefore, pushes the boat upwards. The upward buoyant force is equal to the weight of the **volume** of water displaced by the boat. This is known as Archimedes's principle. A heavy boat will float as long as it has a large enough volume to displace enough water to balance its weight.

External pressure exerted on a fluid is transmitted, undiminished, throughout the fluid. This is known as Pascal's principle. This principle is used in a hydraulic lever in which pressure applied on a small piston is transmitted unchanged to a large piston. Since the force exerted is equal to the pressure times the area of the piston, a small force exerted on the small piston can lift a heavy load placed on the large piston. Hydraulic **jacks**, used to lift cars, are based on this principle (Figure 1).

In a moving fluid some of this static pressure is converted into dynamic pressure due to the **velocity** of the fluid. A fluid moving faster in a pipe has more dynamic pressure and thus exerts less static pressure on the sides. The complete fluid flow equations are so complicated that only recent advances in computational capability

have made it possible to describe fluid flow fairly accurately in some situations. There are, however, many simplified ways to study flow mathematically and obtain a great deal of insight.

The practical science of hydraulics enabled human beings to design water clocks, irrigate **crops**, and build waterwheels long before the mathematical study of fluids was begun. Now, experiment and theory support each other in designing **dams**, underwater tunnels, and hydraulic machines, and in predicting flows in **rivers**, around airplane wings, and in the atmosphere.

See also Aerodynamics.

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