Fluid Dynamics

Summary

Fluid dynamics is an interdisciplinary field concerned with the behavior of gases, air, and water in motion. An understanding of fluid dynamic principles is essential to the work done in aerodynamics. It informs the design of air and spacecraft. An understanding of fluid dynamic principles is also essential to the field of hydromechanics and the design of oceangoing vessels. Any system with air, gases, or water in motion incorporates the principles of fluid dynamics.

Definition and Basic Principles

Fluid dynamics is the study of fluids in motion. Air, gases, and water are all considered to be fluids. When the fluid is air, this branch of science is called aerodynamics. When the fluid is water, it is called hydrodynamics.

The basic principles of fluid dynamics state that fluids are a state of matter in which a substance cannot maintain an independent shape. A fluid will take the shape of its container, forming an observable surface at the highest level of the fluid when it does not completely fill the container. Fluids flow in a continuum, with no breaks or gaps in the flow. They are said to flow in a streamline, with a series of particles following one another in an orderly fashion in parallel with other streamlines. Real fluids have some amount of internal friction, known as viscosity. Viscosity is the phenomenon that causes some fluids to flow more readily than others. It is the reason that molasses flows more slowly than water at room temperature.

Fluids are said to be compressible or incompressible. Water is an incompressible fluid because its density does not change when pressure is applied. Incompressible fluids are subject to the law of continuity, which states that fluid flows in a pipe are constant. This theory explains why the rate of flow increases when the area of the pipe is reduced and vice versa. The viscosity of a fluid is an important consideration when calculating the total resistance on an object.

The point where the fluid flows at the surface of an object is called the boundary layer. The fluid “sticks” to the object, not moving at all at the point of contact. The streamlines further from the surface are moving, but each is impeded by the streamline between it and the wall until the effect of the streamline closest to the wall is no longer a factor. The boundary layer is not obvious to the casual observer, but it is an important consideration in any calculations of fluid dynamics.

Most fluids are Newtonian fluids. Newtonian fluids have a stress-strain relationship that is linear. This means that a fluid will flow around an object in its path and “come together” on the other side without a delay in time. Non-Newtonian fluids do not have a linear stress-strain relationship. When they encounter shear stress, their recovery varies with the type of non-Newtonian fluid.

A main consideration in fluid dynamics is the amount of resistance encountered by an object moving through a fluid. Resistance, also known as drag, is made up of several components, all of which have one thing in common: they occur at the point where the object meets the fluid. The area can be quite large, as in the wetted surface of a ship, the portion of a ship that is below the waterline. For an airplane, the equivalent is the body of the plane as it moves through the air. The goal for those who work in the field of fluid dynamics is to understand the effects of fluid flows and minimize their effect on the object in question.

Background and History

Swiss mathematician Daniel Bernoulli introduced the term “hydrodynamics” with the publication of his book Hydrodynamica in 1738. The name referred to water in motion and gave the field of fluid dynamics its first name, but it was not the first time water in action had been noted and studied. Leonardo da Vinci made observations of water flows in a river and realized that water is an incompressible flow and that for an incompressible flow, V = constant. This law of continuity states that fluid flow in a pipe is constant. In the late 1600s, French physicist Edme Mariotte and Dutch mathematician Christiaan Huygens contributed the velocity-squared law to the science of fluid dynamics. They did not work together, but they both reached the conclusion that resistance is proportional not to velocity itself but to the square of the velocity.

Sir Isaac Newton put forth his three laws of motion in the 1700s. These laws play a fundamental part in many branches of science, including fluid dynamics. In addition to the term hydrodynamics, Bernoulli's contribution to fluid dynamics was the realization that pressure decreases as velocity increases. This understanding is essential to the understanding of lift. Leonhard Euler, the father of fluid dynamics, is considered by many to be the preeminent mathematician of the eighteenth century. He derived what is known as the Bernoulli equation from the work of Daniel Bernoulli. Euler also developed equations for inviscid flows. These equations were based on his own work and are still used for compressible and incompressible fluids.

The Navier-Stokes equations result from the work of French engineer Claude-Louis Navier and British physicist George Gabriel Stokes in the mid-nineteenth century. They did not work together, but their equations apply to incompressible flows. The Navier-Stokes equations are still used. At the end of the nineteenth century, Scottish engineer William John Macquorn Rankine changed the understanding of the way fluids flow with his streamline theory, which states that water flows in a steady current of parallel flows unless disrupted. This theory caused a fundamental shift in the field of ship design because it changed the popular understanding of resistance in oceangoing vessels. Laminar flow is measured by use of the Reynolds number, developed by British engineer and physicist Osborne Reynolds in 1883. When the number is low, viscous forces dominate. When the number is high, turbulent flows are dominant.

American naval architect David Watson Taylor designed and operated the first experimental model basin in the United States at the start of the twentieth century. His seminal work, The Speed and Power of Ships (1910), is still read in the twenty-first century. Taylor played a role in the use of bulbous bows on vessels of the US Navy. He also championed the use of airplanes that would be launched from naval craft underway in the ocean.

The principles of fluid dynamics took to the air in the eighteenth century with the work done by aviators such as the Montgolfier brothers and their hot-air balloons and French physicist Louis-Sébastien Lenormand's parachute. It was not until 1799, when English inventor Sir George Cayley designed the first airplane with an understanding of the roles of lift, drag, and propulsion, that aerodynamics came under scrutiny. Cayley's work was soon followed by the work of American engineer Octave Chanute. In 1875, he designed several biplane gliders, and with the publication of his book Progress in Flying Machines (1894), he became internationally recognized as an aeronautics expert.

The Wright brothers are called the first aeronautical engineers because of the testing they conducted in their wind tunnel. By using balances to test a variety of airfoil shapes, they correctly predicted the lift and drag of different wing shapes. This work enabled them to fly successfully at Kitty Hawk, North Carolina, on December 17, 1903.

German physicist Ludwig Prandtl identified the boundary layer in 1904. His work led him to be known as the father of modern aerodynamics. Russian scientist Konstantin Tsiolkovsky and American physicist Robert Goddard followed, and Goddard's first successful liquid propellant rocket launch in 1926 earned him the title of the father of modern rocketry.

All of the principles that apply to hydrodynamics—the study of water in motion—apply to aerodynamics, the study of air in motion. Together, these principles constitute the field of fluid dynamics.

How It Works

When an object moves through a fluid, such as gas or water, it encounters resistance. How much resistance depends upon the amount of internal friction in the fluid (the viscosity) as well as the shape of the object. A torpedo, with its streamlined shape, will encounter less resistance than a two-by-four that is neither sanded nor varnished. A ship with a square bow will encounter more resistance than one with a bulbous bow and V shape. All of this is important because with greater resistance comes the need for greater power to cover a given distance. Since power requires a fuel source and a way to carry that fuel, a vessel that can travel with a lighter fuel load will be more efficient. Whether the design under consideration is for a tractor-trailer, an automobile, an ocean liner, an airplane, a rocket, or a space shuttle, these basic considerations are of paramount importance in their design.

Applications and Products

Fluid dynamics plays a part in the design of everything from automobiles to rockets. Fluid dynamic principles are also used in medical research by bioengineers who want to know how a pacemaker will perform or what effect an implant or shunt will have on blood flow. Fire flows are also being studied to aid in the science of wildfire management. Previously, the models focused on heat transfer, but in the twenty-first century, studies are looking at fire systems and their fluid dynamic properties. Sophisticated models are used to predict fluid flows before model testing is done. This lowers the cost of new designs and allows the people involved to gain a thorough understanding of the trade-off between size and power, given a certain design and level of resistance.

Careers and Course Work

Fluid dynamics plays a part in a host of careers. Naval architects use fluid dynamic principles to design vessels. Aeronautical engineers use the principles to design aircraft. Astronautical engineers use fluid dynamic principles to design spacecraft. Weapons are constructed with an understanding of fluids in motion. Automotive engineers must understand fluid dynamics to design fuel-efficient cars. Architects must take the motion of air into their design of skyscrapers and other large buildings. Bioengineers use fluid dynamic principles to their advantage in designing components that will interact with blood flow in the human body. Land management professionals can use their understanding of fluid flows to develop plans for protecting the areas under their care from catastrophic loss due to fires. Civil engineers consider the principles of fluid dynamics when designing bridges. Fluid dynamics also plays a role in sports, from pitchers who want to improve their curveballs to quarterbacks who are determined to increase the accuracy of their passes.

Students should take substantial coursework in more than one of the primary fields of study related to fluid dynamics (physics, mathematics, computer science, and engineering) because the fields that depend upon knowledge of fluid dynamic principles draw from multiple disciplines. In addition, anyone desiring to work in fluid dynamics should possess skills beyond academics, including an aptitude for mechanical details and the ability to envision a problem in multiple dimensions. A collaborative mindset is also an asset, as fluid dynamic applications tend to be created by teams.

Social Context and Future Prospects

The science of fluid dynamics touches on several career fields, from sports to bioengineering. Anything that moves through liquids such as air, water, or gases is subject to the principles of fluid dynamics. The more thorough the understanding, the more efficient vessel and other designs will be. This will result in using fewer resources in the form of power for inefficient designs and help create more efficient aircraft, launch vehicles, and medical breakthroughs.

Bibliography

Anderson, John D., Jr. A History of Aerodynamics and Its Impact on Flying Machines. 1997. Cambridge University Press, 2001.

Bhattacharyya, Binoy. Fluid Dynamics. New Central Book Agency, 2020.

Çengel, Yunus A., and John M. Cimbala. Fluid Mechanics: Fundamentals and Applications. 4th ed., McGraw-Hill, 2017.

Darrigol, Olivier. Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl. Oxford University Press, 2005.

Eckert, Michael. The Dawn of Fluid Dynamics: A Discipline Between Science and Technology. Wiley-VCH, 2006.

Ferreiro, Larrie D. Ships and Science: The Birth of Naval Architecture in the Scientific Revolution, 1600–1800. MIT Press, 2007.

Johnson, Richard W., ed. The Handbook of Fluid Dynamics. 2nd ed., CRC Press, 2016.

Mirzaei, Parham A. Computational Fluid Dynamics and Energy Modelling in Buildings: Fundamentals and Applications. Wiley-Blackwell, 2023.

Shivamoggi, Bhimsen K. Introduction to Theoretical and Mathematical Fluid Dynamics. 3rd ed., John Wiley & Sons, 2023. 

Visconti, Guido, and Paolo Ruggieri. Fluid Dynamics: Fundamentals and Applications. Springer, 2020.