# FLUID MECHANICS

## CONCEPT

The term "fluid" in everyday language typically refers only to liquids, but in the realm of physics, fluid describes any gas or liquid that conforms to the shape of its container. Fluid mechanics is the study of gases and liquids at rest and in motion. This area of physics is divided into fluid statics, the study of the behavior of stationary fluids, and fluid dynamics, the study of the behavior of moving, or flowing, fluids. Fluid dynamics is further divided into hydrodynamics, or the study of water flow, and aerodynamics, the study of airflow. Applications of fluid mechanics include a variety of machines, ranging from the water-wheel to the airplane. In addition, the study of fluids provides an understanding of a number of everyday phenomena, such as why an open window and door together create a draft in a room.

## HOW IT WORKS

### The Contrast Between Fluids and Solids

To understand fluids, it is best to begin by contrasting their behavior with that of solids. Whereas solids possess a definite volume and a definite shape, these physical characteristics are not so clearly defined for fluids. Liquids, though they possess a definite volume, have no definite shapea factor noted above as one of the defining characteristics of fluids. As for gases, they have neither a definite shape nor a definite volume.

One of several factors that distinguishes fluids from solids is their response to compression, or the application of pressure in such a way as to reduce the size or volume of an object. A solid is highly noncompressible, meaning that it resists compression, and if compressed with a sufficient force, its mechanical properties alter significantly. For example, if one places a drinking glass in a vise, it will resist a small amount of pressure, but a slight increase will cause the glass to break.

Fluids vary with regard to compressibility, depending on whether the fluid in question is a liquid or a gas. Most gases tend to be highly compressiblethough air, at low speeds at least, is not among them. Thus, gases such as propane fuel can be placed under high pressure. Liquids tend to be noncompressible: unlike a gas, a liquid can be compressed significantly, yet its response to compression is quite different from that of a solida fact illustrated below in the discussion of hydraulic presses.

One way to describe a fluid is "anything that flows"a behavior explained in large part by the interaction of molecules in fluids. If the surface of a solid is disturbed, it will resist, and if the force of the disturbance is sufficiently strong, it will deformas for instance, when a steel plate begins to bend under pressure. This deformation will be permanent if the force is powerful enough, as was the case in the above example of the glass in a vise. By contrast, when the surface of a liquid is disturbed, it tends to flow.

#### MOLECULAR BEHAVIOR OF FLUIDS AND SOLIDS.

At the molecular level, particles of solids tend to be definite in their arrangement and close to one another. In the case of liquids, molecules are close in proximity, though not as much so as solid molecules, and the arrangement is random. Thus, with a glass of water, the molecules of glass (which at relatively low temperatures is a solid) in the container are fixed in place while the molecules of water contained by the glass are not. If one portion of the glass were moved to another place on the glass, this would change its structure. On the other hand, no significant alteration occurs in the character of the water if one portion of it is moved to another place within the entire volume of water in the glass.

As for gas molecules, these are both random in arrangement and far removed in proximity. Whereas solid particles are slow-moving and have a strong attraction to one another, liquid molecules move at moderate speeds and exert a moderate attraction on each other. Gas molecules are extremely fast-moving and exert little or no attraction.

Thus, if a solid is released from a container pointed downward, so that the force of gravity moves it, it will fall as one piece. Upon hitting a floor or other surface, it will either rebound, come to a stop, or deform permanently. A liquid, on the other hand, will disperse in response to impact, its force determining the area over which the total volume of liquid is distributed. But for a gas, assuming it is lighter than air, the downward pull of gravity is not even required to disperse it: once the top on a container of gas is released, the molecules begin to float outward.

### Fluids Under Pressure

As suggested earlier, the response of fluids to pressure is one of the most significant aspects of fluid behavior and plays an important role within both the statics and dynamics subdisciplines of fluid mechanics. A number of interesting principles describe the response to pressure, on the part of both fluids at rest inside a container, and fluids which are in a state of flow.

Within the realm of hydrostatics, among the most important of all statements describing the behavior of fluids is Pascal's principle. This law is named after Blaise Pascal (1623-1662), a French mathematician and physicist who discovered that the external pressure applied on a fluid is transmitted uniformly throughout its entire body. The understanding offered by Pascal's principle later became the basis for one of the most important machines ever developed, the hydraulic press.

#### HYDROSTATIC PRESSURE AND BUOYANCY.

Some nineteen centuries before Pascal, the Greek mathematician, physicist, and inventor Archimedes (c. 287-212 b.c.) discovered a precept of fluid statics that had implications at least as great as those of Pascal's principle. This was Archimedes's principle, which explains the buoyancy of an object immersed in fluid. According to Archimedes's principle, the buoyant force exerted on the object is equal to the weight of the fluid it displaces.

Buoyancy explains both how a ship floats on water, and how a balloon floats in the air. The pressures of water at the bottom of the ocean, and of air at the surface of Earth, are both examples of hydrostatic pressurethe pressure that exists at any place in a body of fluid due to the weight of the fluid above. In the case of air pressure, air is pulled downward by the force of Earth's gravitation, and air along the planet's surface has greater pressure due to the weight of the air above it. At great heights above Earth's surface, however, the gravitational force is diminished, and thus the air pressure is much smaller.

Water, too, is pulled downward by gravity, and as with air, the fluid at the bottom of the ocean has much greater pressure due to the weight of the fluid above it. Of course, water is much heavier than air, and therefore, water at even a moderate depth in the ocean has enormous pressure. This pressure, in turn, creates a buoyant force that pushes upward.

If an object immersed in fluida balloon in the air, or a ship on the oceanweighs less that the fluid it displaces, it will float. If it weighs more, it will sink or fall. The balloon itself may be "heavier than air," but it is not as heavy as the air it has displaced. Similarly, an aircraft carrier contains a vast weight in steel and other material, yet it floats, because its weight is not as great as that of the displaced water.

#### BERNOULLI'S PRINCIPLE.

Archimedes and Pascal contributed greatly to what became known as fluid statics, but the father of fluid mechanics, as a larger realm of study, was the Swiss mathematician and physicist Daniel Bernoulli (1700-1782). While conducting experiments with liquids, Bernoulli observed that when the diameter of a pipe is reduced, the water flows faster. This suggested to him that some force must be acting upon the water, a force that he reasoned must arise from differences in pressure.

Specifically, the slower-moving fluid in the wider area of pipe had a greater pressure than the portion of the fluid moving through the narrower part of the pipe. As a result, he concluded that pressure and velocity are inversely relatedin other words, as one increases, the other decreases. Hence, he formulated Bernoulli's principle, which states that for all changes in movement, the sum of static and dynamic pressure in a fluid remains the same.

A fluid at rest exerts pressurewhat Bernoulli called "static pressure"on its container. As the fluid begins to move, however, a portion of the static pressureproportional to the speed of the fluidis converted to what Bernoulli called dynamic pressure, or the pressure of movement. In a cylindrical pipe, static pressure is exerted perpendicular to the surface of the container, whereas dynamic pressure is parallel to it.

According to Bernoulli's principle, the greater the velocity of flow in a fluid, the greater the dynamic pressure and the less the static pressure. In other words, slower-moving fluid exerts greater pressure than faster-moving fluid. The discovery of this principle ultimately made possible the development of the airplane.

## REAL-LIFE APPLICATIONS

### Bernoulli's Principle in Action

As fluid moves from a wider pipe to a narrower one, the volume of the fluid that moves a given distance in a given time period does not change. But since the width of the narrower pipe is smaller, the fluid must move faster (that is, with greater dynamic pressure) in order to move the same amount of fluid the same distance in the same amount of time. Observe the behavior of a river: in a wide, unconstricted region, it flows slowly, but if its flow is narrowed by canyon walls, it speeds up dramatically.

Bernoulli's principle ultimately became the basis for the airfoil, the design of an airplane's wing when seen from the end. An airfoil is shaped like an asymmetrical teardrop laid on its side, with the "fat" end toward the airflow. As air hits the front of the airfoil, the airstream divides, part of it passing over the wing and part passing under. The upper surface of the airfoil is curved, however, whereas the lower surface is much straighter.

As a result, the air flowing over the top has a greater distance to cover than the air flowing under the wing. Since fluids have a tendency to compensate for all objects with which they come into contact, the air at the top will flow faster to meet the other portion of the airstream, the air flowing past the bottom of the wing, when both reach the rear end of the airfoil. Faster airflow, as demonstrated by Bernoulli, indicates lower pressure, meaning that the pressure on the bottom of the wing keeps the airplane aloft.

#### CREATING A DRAFT.

Among the most famous applications of Bernoulli's principle is its use in aerodynamics, and this is discussed in the context of aerodynamics itself elsewhere in this book. Likewise, a number of other applications of Bernoulli's principle are examined in an essay devoted to that topic. Bernoulli's principle, for instance, explains why a shower curtain tends to billow inward when the water is turned on; in addition, it shows why an open window and door together create a draft.

Suppose one is in a hotel room where the heat is on too high, and there is no way to adjust the thermostat. Outside, however, the air is cold, and thus, by opening a window, one can presumably cool down the room. But if one opens the window without opening the front door of the room, there will be little temperature change. The only way to cool off will be by standing next to the window: elsewhere in the room, the air will be every bit as stuffy as before. But if the door leading to the hotel hallway is opened, a nice cool breeze will blow through the room. Why?

With the door closed, the room constitutes an area of relatively high pressure compared to the pressure of the air outside the window. Because air is a fluid, it will tend to flow into the room, but once the pressure inside reaches a certain point, it will prevent additional air from entering. The tendency of fluids is to move from high-pressure to low-pressure areas, not the other way around. As soon as the door is opened, the relatively high-pressure air of the room flows into the relatively low-pressure area of the hallway. As a result, the air pressure in the room is reduced, and the air from outside can now enter. Soon a wind will begin to blow through the room.

#### A WIND TUNNEL.

The above scenario of wind flowing through a room describes a rudimentary wind tunnel. A wind tunnel is a chamber built for the purpose of examining the characteristics of airflow in contact with solid objects, such as aircraft and automobiles. The wind tunnel represents a safe and judicious use of the properties of fluid mechanics. Its purpose is to test the interaction of airflow and solids in relative motion: in other words, either the aircraft has to be moving against the airflow, as it does in flight, or the airflow can be moving against a stationary aircraft. The first of these choices, of course, poses a number of dangers; on the other hand, there is little danger in exposing a stationary craft to winds at speeds simulating that of the aircraft in flight.

The first wind tunnel was built in England in 1871, and years later, aircraft pioneers Orville (1871-1948) and Wilbur (1867-1912) Wright used a wind tunnel to improve their planes. By the late 1930s, the U.S. National Advisory Committee for Aeronautics (NACA) was building wind tunnels capable of creating speeds equal to 300 MPH (480 km/h); but wind tunnels built after World War II made these look primitive. With the development of jet-powered flight, it became necessary to build wind tunnels capable of simulating winds at the speed of sound760 MPH (340 m/s). By the 1950s, wind tunnels were being used to simulate hypersonic speedsthat is, speeds of Mach 5 (five times the speed of sound) and above. Researchers today use helium to create wind blasts at speeds up to Mach 50.

### Fluid Mechanics for Performing Work

#### HYDRAULIC PRESSES.

Though applications of Bernoulli's principle are among the most dramatic examples of fluid mechanics in operation, the everyday world is filled with instances of other ideas at work. Pascal's principle, for instance, can be seen in the operation of any number of machines that represent variations on the idea of a hydraulic press. Among these is the hydraulic jack used to raise a car off the floor of an auto mechanic's shop.

Beneath the floor of the shop is a chamber containing a quantity of fluid, and at either end of the chamber are two large cylinders side by side. Each cylinder holds a piston, and valves control flow between the two cylinders through the channel of fluid that connects them. In accordance with Pascal's principle, when one applies force by pressing down the piston in one cylinder (the input cylinder), this yields a uniform pressure that causes output in the second cylinder, pushing up a piston that raises the car.

Another example of a hydraulic press is the hydraulic ram, which can be found in machines ranging from bulldozers to the hydraulic lifts used by firefighters and utility workers to reach heights. In a hydraulic ram, however, the characteristics of the input and output cylinders are reversed from those of a car jack. For the car jack, the input cylinder is long and narrow, while the output cylinder is wide and short. This is because the purpose of a car jack is to raise a heavy object through a relatively short vertical range of movementjust high enough so that the mechanic can stand comfortably underneath the car.

In the hydraulic ram, the input or master cylinder is short and squat, while the output or slave cylinder is tall and narrow. This is because the hydraulic ram, in contrast to the car jack, carries a much lighter cargo (usually just one person) through a much greater vertical rangefor instance, to the top of a tree or building.

#### PUMPS.

A pump is a device made for moving fluid, and it does so by utilizing a pressure difference, causing the fluid to move from an area of higher pressure to one of lower pressure. Its operation is based on aspects both of Pascal's and Bernoulli's principlesthough, of course, humans were using pumps thousands of years before either man was born.

A siphon hose used to draw gas from a car's fuel tank is a very simple pump. Sucking on one end of the hose creates an area of low pressure compared to the relatively high-pressure area of the gas tank. Eventually, the gasoline will come out of the low-pressure end of the hose.

The piston pump, slightly more complex, consists of a vertical cylinder along which a piston rises and falls. Near the bottom of the cylinder are two valves, an inlet valve through which fluid flows into the cylinder, and an outlet valve through which fluid flows out. As the piston moves upward, the inlet valve opens and allows fluid to enter the cylinder. On the downstroke, the inlet valve closes while the outlet valve opens, and the pressure provided by the piston forces the fluid through the outlet valve.

One of the most obvious applications of the piston pump is in the engine of an automobile. In this case, of course, the fluid being pumped is gasoline, which pushes the pistons up and down by providing a series of controlled explosions created by the spark plug's ignition of the gas. In another variety of piston pumpthe kind used to inflate a basketball or a bicycle tireair is the fluid being pumped. Then there is a pump for water. Pumps for drawing usable water from the ground are undoubtedly the oldest known variety, but there are also pumps designed to remove water from areas where it is undesirable; for example, a bilge pump, for removing water from a boat, or the sump pump used to pump flood water out of a basement.

#### FLUID POWER.

For several thousand years, humans have used fluidsin particular waterto power a number of devices. One of the great engineering achievements of ancient times was the development of the waterwheel, which included a series of buckets along the rim that made it possible to raise water from the river below and disperse it to other points. By about 70

b.c., Roman engineers recognized that they could use the power of water itself to turn wheels and grind grain. Thus, the waterwheel became one of the first mechanisms in which an inanimate source (as opposed to the effort of humans or animals) created power.

The water clock, too, was another ingenious use of water developed by the ancients. It did not use water for power; rather, it relied on gravitya concept only dimly understood by ancient peoplesto move water from one chamber of theclock to another, thus, marking a specific interval of time. The earliest clocks were sundials, which were effective for measuring time, provided the Sun was shining, but which were less useful form easuring periods shorter than an hour. Hence, the development of the hourglass, which used sand, a solid that in larger quantities exhibits the behavior of a fluid. Then, in about 270 b.c., Ctesibius of Alexandria (fl. c. 270-250 b.c.) used gearwheel technology to devise a constant-flow water clock called a "clepsydra." Use of water clocks prevailed for more than a thousand years, until the advent of the first mechanical clocks.

During the medieval period, fluids provided power to windmills and water mills, and at the dawn of the Industrial Age, engineers began applying fluid principles to a number of sophisticated machines. Among these was the turbine, a machine that converts the kinetic energy (the energy of movement) in fluids to useable mechanical energy by passing the stream of fluid through a series of fixed and moving fans or blades. A common house fan is an example of a turbine in reverse: the fan adds energy to the passing fluid (air), whereas a turbine extracts energy from fluids such as air and water.

The turbine was developed in the mid-eighteenth century, and later it was applied to the extraction of power from hydroelectric dams, the first of which was constructed in 1894. Today, hydroelectric dams provide electric power to millions of homes around the world. Among the most dramatic examples of fluid mechanics in action, hydroelectric dams are vast in size and equally impressive in the power they can generate using a completely renewable resource: water.

A hydroelectric dam forms a huge steel-and-concrete curtain that holds back millions of tons of water from a river or other body. The water nearest the topthe "head" of the damhas enormous potential energy, or the energy that an object possesses by virtue of its position. Hydroelectric power is created by allowing controlled streams of this water to flow downward, gathering kinetic energy that is then transferred to powering turbines, which in turn generate electric power.

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## KEY TERMS

### AERODYNAMICS:

An area of fluid dynamics devoted to studying the properties and characteristics of airflow.

### ARCHIMEDES'S PRINCIPLE:

A rule of physics stating that the buoyant force of an object immersed in fluid is equal to the weight of the fluid displaced by the object. It is named after the Greek mathematician, physicist, and inventor, Archimedes (c.287-212 b.c.), who first identified it.

### BERNOULLI'S PRINCIPLE:

A proposition, credited to Swiss mathematician and physicist Daniel Bernoulli (1700-1782), which maintains that slower-moving fluid exerts greater pressure than faster-moving fluid.

### BUOYANCY:

The tendency of an objectimmersed in a fluid to float. This can be explained by Archimedes's principle.

### COMPRESSION:

To reduce in size or volume by applying pressure.

### FLUID:

Any substance, whether gas or liquid, that conforms to the shape of itscontainer.

### FLUID DYNAMICS:

An area of fluid mechanics devoted to studying of the behavior of moving, or flowing, fluids. Fluid dynamics is further divided into hydrodynamics and aerodynamics.

### FLUID MECHANICS:

The study of the behavior of gases and liquids at rest and in motion. The major divisions of fluid mechanics are fluid statics and fluid dynamics.

### FLUID STATICS:

An area of fluid mechanics devoted to studying the behavior of stationary fluids.

### HYDRODYNAMICS:

An area of fluid dynamics devoted to studying the properties and characteristics of water flow.

### HYDROSTATIC PRESSURE:

The pressure that exists at any place in a body of fluid due to the weight of the fluid above.

### PASCAL'S PRINCIPLE:

A statement, formulated by French mathematician and physicist Blaise Pascal (1623-1662), which holds that the external pressure applied on a fluid is transmitted uniformly throughout the entire body of that fluid.

### PRESSURE:

The ratio of force to surface area, when force is applied in a direction perpendicular to that surface.

### TURBINE:

A machine that converts the kinetic energy (the energy of movement) in fluids to useable mechanical energy by passing the stream of fluid through a series of fixed and moving fans or blades.

### WIND TUNNEL:

A chamber built for the purpose of examining the characteristics of airflow in relative motion against solid objects such as aircraft and automobiles.

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## fluid mechanics

fluid mechanics, branch of mechanics dealing with the properties and behavior of fluids, i.e., liquids and gases. Because of their ability to flow, liquids and gases have many properties in common not shared by solids. The special study of fluids in motion, or fluid dynamics, makes up the larger part of fluid mechanics. Branches of fluid dynamics include hydrodynamics (study of liquids in motion) and aerodynamics (study of gases in motion). Hydrodynamics is often used synonymously with fluid dynamics, since most of the results from the study of liquids also apply to gases. A plasma is also a fluid (see states of matter) and can be described by many of the principles of fluid mechanics, but its electromagnetic properties must also be taken into account. The study of plasmas in motion is known as magnetohydrodynamics and includes principles from several fields.

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## fluid mechanics

fluid mechanics Study of the behaviour of liquids and gases. Fluid statics is the study of fluids at rest and includes the study of pressure, density and the principles of Pascal and Archimedes. Fluid dynamics is the study of moving fluids and includes the study of streamline flow, Bernoulli's law (used to measure a fluid's velocity) and the propagation of waves. Engineers use fluid mechanics in the design of bridges, dams and ships. Aerodynamics, the study of the motion of gases, and hydrodynamics, the study of the motion of liquids, are branches of fluid mechanics.