Fluid dynamics is the study of the flow of liquids and gases, usually in and around solid surfaces. For example, fluid dynamics can be used to analyze the flow of air over an airplane wing or over the surface of an automobile. It also can be used in the design of ships to increase the speed with which they travel through water.

Scientists use both experiments and mathematical models and calculations to understand fluid dynamics. A wind tunnel is an enclosed space in which air can be made to flow over a surface, such as the model of an airplane. Smoke is added to the air stream so that the flow of air can be observed and photographed.

The data collected from wind tunnel studies and other experiments are often very complex. Scientists today use models of fluid behavior and powerful computers to analyze and interpret those data.

The field of fluid dynamics is often subdivided into aerodynamics and hydrodynamics. Aerodynamics is the study of the way air flows around airplanes and automobiles with the aim of increasing the efficiency of motion. Hydrodynamics deals with the flow of water in various situations such as in pipes, around ships, and underground. Apart from the more familiar cases, the principles of fluid dynamics can be used to understand an almost unimaginable variety of phenomena such as the flow of blood in blood vessels, the flight of geese in V-formation, and the behavior of underwater plants and animals.

Flow patterns in a fluid (gas or liquid) depend on three factors: the characteristics of the fluid, the speed of flow, and the shape of the solid surface. Three characteristics of the fluid are of special importance: viscosity, density, and compressibility. Viscosity is the amount of internal friction or resistance to flow. Water, for instance, is less viscous than honey, which explains why water flows more easily than does honey.

All gases are compressible, whereas liquids are practically incompressible; that is, they cannot be squeezed into smaller volumes. Flow patterns in compressible fluids are more complicated and difficult to study than those in incompressible ones. Fortunately for automobile designers, at speeds less than about 220 miles (350 kilometers) per hour, air can be treated as incompressible for all practical purposes. Also, for incompressible fluids, the effects of temperature changes can be neglected.

**Boundary layer:** The layer of fluid that sticks to a solid surface and through which the speed of the fluid decreases.

**Compressibility:** The property that allows a fluid to be compressed into a smaller volume.

**Laminar:** A mode of flow in which the fluid moves in layers along continuous, well-defined lines known as streamlines.

**Turbulent:** An irregular, disorderly mode of flow.

**Viscosity:** The internal friction within a fluid that makes it resist flow.

Flow patterns can be characterized as laminar or turbulent. The term laminar refers to streamlined flow in which a fluid glides along in layers that do not mix. The flow takes place in smooth continuous lines called streamlines. You can observe this effect when you open a water faucet just a little so that the flow is clear and regular. If you continue turning the faucet, the flow gradually becomes cloudy and irregular. This condition is known as turbulent flow.

The Mach number is a measurement used in fluid dynamics that compares the velocity of an object traveling through a fluid to the speed of sound in that fluid. For example, the speed of sound in air at sea level at a temperature of 59°F (15°C) is about 760 miles per hour (340 meters per second). Imagine an airplane flying just above the ocean at a speed of 380 miles per hour (170 meters per second). In that case, the Mach number of the airplane would be 380 miles per hour divided by 760 miles per hour (380 mph ÷ 760 mph) or 0.5.

The Mach number is named after Austrian physicist and philosopher Ernst Mach (1838–1916), who pioneered the study of supersonic (faster than sound) travel. The Mach number is especially important in the field of fluid dynamics because fluids flow around an object in quite different ways. For example, when an airplane flies at a speed greater than the speed of sound, sound waves are not able to "get out of the way" of the airplane. Shock waves are produced, resulting in the sonic booms heard when an airplane exceeds the speed of sound.

Aircraft designers have to take differences in fluid behavior at different Mach numbers into account when designing planes that take off and climb to altitude at speeds in the subsonic (less than the speed of sound) region, then pass through the transonic (about equal to the speed of sound) region, and cruise at speeds in the supersonic region.

**Bernoulli's principle.** Swiss mathematician Daniel Bernoulli (1700–1782) was the first person to study fluid flow mathematically. For his research, Bernoulli imagined a completely nonviscous and incompressible or "ideal" fluid. In this way, he did not have to worry about all the many complications that are present in real examples of fluid flow. The mathematical equations Bernoulli worked out represent only ideal situations, then, but they are useful in many real-life situations.

A simple way to understand Bernoulli's result is to picture water flowing through a horizontal pipe with a diameter of 4 inches (10 centimeters). Then imagine a constricted section in the middle of the pipe with a diameter of only 2 inches (5 centimeters). Bernoulli's principle says that water flowing through the pipe has to speed up in the constricted portion of the pipe. If water flowed at the same rate in the constricted portion of the pipe, less water would get through. The second half of the pipe would not be full.

What Bernoulli showed was that water in the constricted section of the pipe (through which liquid moves more quickly) experiences less water pressure. Suppose the water pressure in the wide part of the pipe is 20 newtons per square meter. Then the pressure in the constricted part of the pipe might be only 15 newtons per square meter. More generally, Bernoulli's principle says that the pressure exerted by a fluid decreases as the velocity of that fluid increases.

Bernoulli's principle is easy to demonstrate. Hold both ends of a piece of paper in your two hands and blow over the upper surface of the paper. The paper appears to rise, as if by magic. The "magic" is that air passing over the surface of the paper causes reduced pressure from above on the paper. Normal atmospheric pressure below the paper pushes it upward. This simple demonstration also illustrates the principle on which airplanes fly. Air flying over the wings of the airplane produces a lifting effect from below on the wings.

**Boundary layer effects.** Bernoulli's principle works very well in many cases. But assuming that fluids have no viscosity, as Bernoulli did, does introduce some errors in real life. The reason for these errors is that even in fluids with very low viscosity, the fluid right next to the solid boundary sticks to the surface. This effect is known as the no-slip condition. Thus, however fast or easily the fluid away from the boundary may be moving, the fluid near the boundary has to slow down gradually and come to a complete stop exactly at the boundary. This effect is what causes drag on automobiles and airplanes in spite of the low viscosity of air.

The treatment of such flows was considerably simplified by the boundary layer concept introduced by German physicist Ludwig Prandtl (1875–1953) in 1904. According to Prandtl, a fluid slows down only in a thin layer next to the surface. This boundary layer starts forming at the beginning of the flow and slowly increases in thickness. It is laminar in the beginning but becomes turbulent after some period of time. Since the effect of viscosity is confined to the boundary layer, the fluid away from the boundary may be treated as ideal.

**Shape and drag.** Moving automobiles and airplanes experience a resistance or drag due to the viscous force of air sticking to their surface. Another source of resistance is pressure drag, which is due to a phenomenon known as flow separation. This happens when there is an abrupt change in the shape of the moving object, and the fluid is unable to make a sudden change in flow direction and stay with the boundary. In this case, the boundary layer gets detached from the body, and a region of low pressure turbulence or wake is formed below it, creating a drag on the vehicle (due to the higher pressure in the front). That is why aerodynamically designed cars are shaped so that the boundary layer remains attached to the body longer, creating a smaller wake and, therefore, less drag. There are many examples in nature of shape modification for drag control. The sea anemone, for instance, with its many tentacles, continuously adjusts its form to the ocean currents in order to avoid being swept away while gathering food.