Fluid Mechanics and Aerodynamics

Type of physical science: Classical physics

Field of study: Fluids

Fluid mechanics and aerodynamics deal with the behavior of fluids in motion and at rest. How fluids influence objects, such as vehicles or animals, which pass through them is important in understanding the complex interactions involved in processes such as flight. Insights gained into fluid behavior possess valuable applications in fields as diverse as aerospace engineering, hydraulics, power plant design, and meteorology.

Overview

The branch of classical physics that concerns itself with the study of the behavior of fluids both at rest and in motion is called fluid mechanics. To physicists, substances that are classified as fluids have specific and unique properties. These material properties are special characteristics of fluids, which among other things, constitute a separate state of matter distinct from other states such as solids. These properties are reactions to known natural processes sometimes termed "physical laws." The primary property of fluids--and that which is their most distinguishing feature--is their ability to flow. While this statement may seem self-evident and redundant, a rigorous and comprehensive definition of the flow phenomenon proved to be a complex proposition that involved centuries of refinement by physicists. For example, fluid mechanics considers both gases and liquids to be fluids, as well as more solid-appearing substances such as glasses, whether artificial such as window glass or natural such as obsidian.

Specifically, fluids are understood to be substances that deform--that is, continuously change their shape or distort--under the application of a shear stress. Shear stress is an opposing force acting perpendicular to the surface or outer boundary of the original body of matter in question, regardless of whether the body is a solid or a fluid. An additional characteristic of a fluid is that it will deform to some degree from shear stress, no matter how small the amount of shear stress applied. Shear stress on a body, whether solid or fluid, can be expressed mathematically in terms of rates of angular deformation. Fluids that behave in a regular, constant manner to shear stress and that experience a reaction that can be expressed by an equation employing a "constant of proportionality," are said to be "Newtonian fluids" in honor of Sir Isaac Newton, who initially formulated this equation regarding fluid friction. This constant is termed "absolute viscosity" or "dynamic viscosity." Many common fluids such as air and water belong to the class of Newtonian fluids, at least at normally encountered states (average atmospheric temperatures and pressures). Nevertheless, a number of fluids exist that are non-Newtonian; among them are human blood and many types of lubricating oils and suspensions. This results from the fact that such materials react to shear force in more complex ways: for example, changing their viscosity over time, either by decreasing or increasing.

The most important considerations involved in classical fluid mechanics equations are viscosity, pressure, compressibility, temperature, density and specific volume, and surface tension. Viscosity, the state of internal friction of any particular fluid, typically acts as a force to inhibit the ability of a substance to flow. Pressure, concerning fluids, can be regarded as a force per unit area or the effect of force acting on a particular surface of a fluid element.

Compressibility is the ability of a given volume of a gas or liquid to be squeezed into a smaller unit area. Temperature can be regarded as the effect of heat or cold upon fluids (and, consequently, their viscosity). Density can be regarded as the amount of fluid per unit volume at a given temperature and pressure. Specific volume can be regarded as the reciprocal of the density. Surface tension is a property unique to fluids, where the fluid surface is in a state of stress and can sometimes support the weight of certain objects without sinking. Surface tension in fluids is dependent on temperature and on the composition and state of the substance upon which it is bounding.

Additional important factors concerning fluids involve properties of internal flow. The internal flow structure of a fluid is typically dichotomized along lines of whether a particular flow is laminar or turbulent. In laminar flow situations, a fluid, such as water, is observed to move in a relatively smooth, harmonious, and uniform manner. The fluid typically has a glassy, smooth appearance and is considered to be moving in layers. As the velocity of the fluid increases, the flow abruptly becomes very disturbed or turbulent. It reaches a critical threshold, where the dominant flow regime is chaotic in nature and the viscosity of the fluid, instead of being relatively uniform as in laminar flow, persists instead in flowing along in a state where viscosity wildly fluctuates. Turbulent flow occurs in both common liquids and gases and is of great importance in understanding many applications of fluid mechanics theory, such as in aeronautics and meteorology.

A fluid's internal friction, shear stress, pressure, and types of flow structure are integrated theoretically in the concept of the "boundary layer," first formulated in Europe at the beginning of the twentieth century. The main elements of the concept postulate that in any flow of fluid molecules over an object, frictional effects are confined to a very thin layer (the boundary layer) found near the surface of an object; the fluid flow external to the boundary is relatively frictionless compared with the boundary layer; and a pressure variation from the main flow of the fluid is "impressed" upon the mainstream and affects the behavior of the boundary layer. The boundary layer interpretation assumes that no matter how smooth the surface of an object that a fluid flow is passing over or around, the molecules of the fluid in actual contact with the surface will remain static. A second, more external layer will be sandwiched between the outermost, normal, main fluid flow and the static flow at a reduced flow velocity. Finally, the third and outermost, "normal" fluid flow will be essentially unaffected in any way, sufficiently away from the boundary layer. In other words, a fluid velocity gradient is produced each time another object's surface comes into contact with a fluid flow. In a typical airstream, such as one produced on the surface of a moving aircraft, the velocity gradient produced is normally a small fraction of a centimeter thick.

As the velocity of a fluid flow increases across or around another surface, such as air over an aircraft airframe or water within the confines of a water pipe or narrow streambed, shear stresses of fluid molecule against fluid molecule increase at the boundary layer. If the fluid velocity increases still further, successive layers of fluid molecules will begin to build up over the boundary layer and a transitional point will be reached where flow is no longer laminar in the boundary layer but inclining more and more toward increased turbulent flow and increased friction. The outcome will eventually be the creation of highly turbulent flow, with rolling vortices and eddies of fluid indicative of chaotic viscosity and flow structure. Such flow structures are graphically familiar in the water patterns observed in rushing streams and brooks.

With regard to vehicles designed for travel in a fluid medium such as air or water, evident turbulent flow is typically symptomatic of design inadequacies regarding hull and control surfaces, which are inefficient and waste fuel because of increased friction.

Fluid mechanics theory has engendered a younger offshoot termed aerodynamics, a sub-branch that deals with the physics of gases and their interactions with moving objects such as vehicles. Like classical fluid mechanics, aerodynamics utilizes the principles of Newtonian physics (various laws of motion) and the principles of thermodynamics (concepts of heat and work, properties of substances in relation to heat and work involved in various processes, and theoretical analysis and mathematical expression of such relationships) to solve problems by rigorously describing phenomena and analyzing processes. Unlike pure fluid mechanics, aerodynamics deals with the realm of fluids restricted to gases (not both gases and liquids). Much of the work that has been done in the last century has been devoted, rather predictably, to the practical applications and problems involved in heavier-than-air manned flight, as the twentieth century has witnessed a rapid and explosive development of that field.

The basic flight equation regarding powered flight involves four basic factors: lift, weight, drag, and thrust. Successful, sustained, controlled flying involves the balance of these four forces. An aircraft, or any animal that has evolved successfully into a powered flyer, whether mammal, bird, or insect, uses these four forces in conjunction with some type of airfoil, a structure that acts as a lifting body, such as wings, which maximize downwash and lift by their shape and angle of attack. The angle of attack of the lifting body is simply the angle at which a body or structure such as a wing meets the airstream in which it is functioning. This angle is not synonymous with or necessarily parallel to the ground. Having a functional airfoil and having the airfoil oriented properly with respect to the angle of attack, a flying animal or machine must cope with the force of drag: the force with which the air resists the motion of an object through it.

Drag is a product of friction, as is lift; however, drag can be classified with regard to powered flying objects in two important, functional ways: It can be regarded as either parasitic or induced.

Induced drag is the useful and necessary drag found over the upper, curved surface of a properly designed (or evolved) airfoil or wing while it is in motion. Parasitic drag is the friction of the airflow over the main body of an animal or machine that is not contributing directly to lift (tail, head, or other protuberances). The difference in velocities and ratios of friction of airflows over the wing surface in such airfoils creates the lift necessary for flight. Lift is the utilized force that acts to raise a wing upward (and simultaneously the main body of a vehicle or animal) created by the formation of a pressure difference, which is produced by wing geometry between air moving at different speeds above and below the wing. Drag can be reduced to varying extents by streamlining or by the designed or evolved reduction of drag by making a vehicle or animal's main body and other structures less turbulence-producing. Thrust is the force that takes advantage of the airflow that acts to move an object, such as an aircraft, forward, regardless of mode of propulsion. The weight factor of the equation is the pull of gravity on the entire flying system that lift attempts to overcome.

Applications

There are myriad useful applications that are direct and indirect products of the complementary fields of fluid mechanics and aerodynamics. Indeed, over the centuries, the intended and unintended processes, techniques, and industries that have been generated by this realm of scientific inquiry have become so pervasive as to become virtually synonymous with Western industrial society.

Essential, practical applications include power generation. The field of pure power generation--whether for electrical consumption for domestic or industrial use--owes a tremendous debt to the field of fluid mechanics by way of the many devices that are in constant, widespread, global use to generate power. Gravity- or tidal-fed hydroelectric turbines are mammoth installations using electromechanical devices that are direct spinoffs of fluid mechanic theory. The design of the intake ducts, outlets, piping, conduits, and the blades themselves are the concrete result of fluid mechanics. Along the same vein, the cooling systems of nuclear reactor-powered, electrical generating stations are likewise the progeny of fluid mechanics. They involve coolant systems and steam-driven electrical turbines. A portable, mobile version of the nuclear-generating station also exists in hundreds of examples beneath the earth's oceans in the form of nuclear-powered submarines. The ubiquitous elevator, garage door lift, and countless smaller, similar devices utilizing hydraulic lifters also can be traced initially to fluid mechanics.

In fact, when closely analyzed, the internal combustion engine itself, whether fueled by diesel, alcohol or jet fuel, is a direct by-product of conceptual paths generated by fluid mechanics.

Along raw power generating lines, one thinks of the rotor-powered wind turbine used increasingly in some areas for electricity production. The easiest paths to trace are those that originate from technology produced for flight itself from aerodynamic theory. One could list the vast industries manufacturing passenger, military, and research aircraft (both propeller and jet-driven, and rotary and fixed wing) and those servicing and being serviced by powered aircraft: tourism, air mail and product shipment, air ambulances, rescue and recovery aircraft, and so on. One of the least appreciated by-products of aerodynamics and fluid mechanics is the great strides taken in weather and climate prediction and meteorology, which also owe their existence to the pioneering and ongoing mathematical modeling of weather systems and processes--physics of fluid masses on a grand scale.

Context

The genesis of fluid mechanics and aerodynamics can be effectively traced to the earliest recorded naturalists and inventors who used logic and empirical observation to try to understand phenomena they witnessed around them. Records from the first century show that the famous Roman naturalist and writer Pliny observed the effect of oil floating on water and speculated on the reasons for such behavior. Several centuries earlier, Hero of Alexandria, a Macedonian Greek living in Egypt, built a working model of a small, steam-driven engine. A Greek philosopher of the fifth century B.C., Empedocles, described the functioning of a mechanical water clock and made accurate conclusions about the air resistance of water pressure.

Despite the speculations and inventions of other ancients such as Archimedes and his original, practical device of a hydraulic lifting screw, it was not until the European Renaissance that a significant insight into fluid mechanics developed. Experimental equipment needed to be devised and basic concepts regarding the true nature of natural phenomenon and the states of matter had to be worked out. A solid step in this direction took place when the seventeenth century Italian scientist Evangelista Torricelli invented a simple but effective barometer and worked out fairly accurately the amount of atmospheric pressure.

In the late seventeenth century, Sir Isaac Newton of England achieved a grand synthesis of empirical knowledge, mathematics, and logic to bring observable facts together in a manner that laid the cornerstone of modern scientific and mathematical thought. The modern science of physics, including that of fluid mechanics and aerodynamics, owes its existence to Newtonian physics. Other physicists refined and improved upon the experiments, observations, and theories of their contemporaries. The twentieth century saw further contributions, such as the German aerodynamicist, Ludwig Prandtl, author of the concept of the boundary layer, which has been such a cornerstone of modern physics theory and engineering.

Principal terms

AIRFOIL: a structure that acts as a lifting body, such as certain wings that have evolved or been designed to maximize downwash and lift by their shape and angle of attack

ANGLE OF ATTACK: the angle at which a body or structure, such as a wing, meets the airstream or fluid stream of whatever medium in which it is functioning

DRAG: the force with which a liquid medium, such as air or water, resists the motion of an object through it; can be classified as either parasitic or induced

FLOW: the motion of a fluid; more concrete, the behavior of a fluid substance, such as water or air, which deforms continuously, that is, changes its shape, in response to a shearing stress, no matter how small

LIFT: a force that acts to raise a wing, created by the formation of a pressure difference and by wing geometry, between air or another fluid moving at different speeds above and below the wing

STREAMLINING: the designed or evolved reduction of drag by making a vehicle or animal's main body and other structures less turbulence-producing

THRUST: any force that acts to move an object forward, such as an aircraft, regardless of mode of propulsion

VISCOSITY: the internal friction of a fluid that acts as a force to inhibit flow; can be classified as either absolute or kinematic

Bibliography

Bernardo, James V. AVIATION AND SPACE IN THE MODERN WORLD. New York: E. P. Dutton, 1968. Describes the many developments in aviation and aerospace technology. Bernardo explains concepts germane to each technology in question. The most pertinent discussion for readers in aerodynamics is chapter 11, "The Facts of Flight," which explains the forces at work and how they are manipulated in various types of aircraft, control surfaces, and devices. Simple formulas, coupled with clearly understandable diagrams, explain how airfoils achieve lift and how they are controlled in flight. A good source of information for readers with little foundation in the physical sciences.

Chow, Chuen-Yen, and Arnold M. Kuethe. FOUNDATIONS OF AERODYNAMICS. New York: John Wiley & Sons, 1986. A thorough treatment of the physical principles of the complex field of aerodynamics, with an emphasis on how natural forces affect the design and performance of heavier-than-air self-propelled aircraft. A good departure point for an in-depth understanding of the field of aircraft engineering. The authors have produced a clearly written but lengthy book on the subject with voluminous diagrams and equations to augment the text. The book, however, is not for those weak in science or mathematics but is geared for advanced high school or college students with a solid background in physics and its supporting mathematics.

Dalton, Stephen. THE MIRACLE OF FLIGHT. New York: McGraw-Hill, 1977. A wonderful addition to anyone's library on the subject of flight and aerodynamics. Examines aerodynamic design and performance of both animals and manned aircraft from a functional perspective in chapter 1, "Fundamentals of Flight." Bird and insect flight are discussed at length, including theories about the evolution of flight and flight-oriented morphology among these groups (chapters 2 and 3). The influence of animal flight structures on the development of manned aircraft design is logically discussed in chapter 4. Chapter 5, "Aircraft of the Twentieth Century," clearly explains details of modern aeronautical design with many concrete examples. A useful informational source for all audiences.

Giancoli, Douglas C. THE IDEAS OF PHYSICS. 2d ed. New York: Harcourt Brace Jovanovich, 1978. A successful attempt at producing a high school or college introductory physics text designed specifically for those who have no background in physics or for those with minimal mathematics background. The text is a highly informative work that avoids complex equations and technical language. In particular, chapters 3, 7, 9, and 10 are most pertinent to readers interested in fluid mechanics and aerodynamics. Suitable for all readers.

Haggerty, James J., and H. Guyford Stever. FLIGHT. New York: Time-Life Books, 1965. A beautifully illustrated introduction to the general subject of flight with chapter 3, "The Science of Aerodynamics," being of primary interest to audiences seeking more information on the physics behind the phenomenon. Ample drawings, diagrams, and color photographs efficiently and enjoyably explain how controlled flight is achieved and maintained. Recommended to all readers at the high school level and above.

Hansen, Arthur G. FLUID MECHANICS. New York: John Wiley & Sons, 1967. A lengthy and comprehensive treatment suitable for readers with a solid foundation in both the physical sciences and mathematics. Chapter 1, "Fundamental Concepts and Fluid Properties," is an excellent introduction to the fundamental concepts involved and contains basic definitions of key terms. The text is augmented by numerous diagrams and equations.

Lapp, Ralph E. MATTER. New York: Time-Life Books, 1969. Designed as an introduction to the general subject of the physics of matter. Chapters are devoted to the various properties of different classes of matter on the atomic and molecular level as well as the liquid, solid, and gaseous states they can assume. Chapters 3 and 4 are relevant. Beautifully illustrated. Recommended reading for audiences high school level and above.

Makower, Joel, ed. THE AIR AND SPACE CATALOG. New York: Vintage Books, 1989. A resource book that is a compendium of useful information and further references dealing with aviation, weather, spaceflight, and astronomy. A useful and handy source. Profusely illustrated, with both black-and-white and color photographs. Appropriate for readers at all levels.

MacAulay, David. THE WAY THINGS WORK. Boston: Houghton Mifflin, 1988. An excellent treatment of the diverse spectrum of natural physical phenomena explained in connection with the realm of inventions. How technological devices exploit forces and processes to do work, including those of fluid mechanics and aerodynamics, is discussed with great lucidity. These discussions are greatly enhanced and expanded upon by myriad original drawings. Both text and illustrations explain the basic concepts and hardware involved in aircraft, submarines, pumping devices, and engines. A good basic, introductory book for readers without any foundation in the physical sciences or the technologies they have engendered.

Tritton, D. J. PHYSICAL FLUID MECHANICS. New York: Van Nostrand Reinhold, 1977. A physics text that emphasizes concepts over mathematical elaborations. Much of the book is suitable for readers with a solid foundation in both the physical sciences and mathematics. The text is enhanced by numerous diagrams, equations, and some photographs.

The Behavior of Gases

Laws of Thermodynamics