Reynolds number

The Reynolds number (Re) is an equation in fluid mechanics. The Re helps predict similar flow patterns in different fluid flow situations. Fluid mechanics is a branch of physics that studies liquids, gases, and plasmas and the forces affecting them. The work of mechanical engineers and chemical engineers in geophysics, astrophysics, and biology is based on fluid mechanics. The Reynolds number is the ratio of inertial forces to viscous forces, i.e., the measure of resistance to deformation by shear or tensile stress. Honey is thicker than water because its viscosity is greater than water’s. The Reynolds number quantifies the inertial and viscous forces for flow conditions. For instance, low Re occurs when viscous forces are dominant, and fluid motion is smooth and constant. Re numbers are high in turbulent flow dominated by inertial forces producing eddies (swirling and reverse flows such as two currents colliding) and vortices (fluids rotating around an axis like the vortex created by the passage of an aircraft wing).

Background

George Stokes, an Irish-born physicist and mathematician, introduced the Reynolds number in 1851, but the concept was not named after him. In 1883, the concept was named the Reynolds number after Osborne Reynolds. He popularized it by demonstrating its applicability as a guide in physics, but not as a guarantee of similitude. His was as an equation serving as guide for estimating chaotic fluid flow in two types: laminar and turbulent. The Re identifies the common characteristic among the length, velocity, density, and viscosity of the fluid being tested. The work of Stokes led to advances in fluid dynamics (liquids and gases in motion) and physical optics used in optics, engineering, and applied physics. While Stokes was an eminent theorist, Osborne Reynolds was the applications innovator. He applied the concept to heat transfer between solids and fluids that led to improvements in boiler and condenser designs. An Irishman working at the University of Manchester, he became the eponymous hero of fluid mechanics measuring turbulent flows. Ship designers used the Reynolds number making small-scale models and extrapolating predictive data to a full size ship; they applied Reynolds’ turbulence principles to friction and drag calculations.

Reynold’s was trying to decipher the universe using the Reynolds number, but few were able to comprehend this aspect of Reynolds’ work. He also studied other complex systems, such as the relationship between motion and surface of a fluid and velocity and a characteristic length or dimension (a fluid in a pipe or sphere and other shapes). Airplane manufacturing was a burgeoning industry, and the Reynolds number contributed to improvements in airfoil (wing) design. The Re made possible the broad range of uses of synthetic and natural polymers. Polymers are the basis for plastics, DNA, and proteins. The Reynolds number is used in mixing or compounding polymers producing physical properties including toughness, viscoelasticity, and more. The Reynolds number was applied to blood circulation dependent on laminar flow (the streamlined way blood flows), helping detect high and low blood pressures due to the turbulent flow of blood. This practical application for the Reynolds number grew from an early experiment he conducted examining the flow of fluids through wide passage in high velocity flows.

Reynolds Number Today

In the twenty-first century, the Reynolds number contributes to space flight and the zap in ray guns by an experiment in which Reynolds introduced a fine filament of dye to the flow of water through a glass tube studying the flows. The filament appeared as a straight line in low velocities through the length of the tube (laminar flow). Increasing the velocity of the dye, he discovered the filament becomes wavy indicating transition flow. Faster, the filament breaks apart and diffuses in the water in the glass tube indicating turbulent flow. This led to the Reynolds number contribution to space travel. Subsequent scientists discovered they were able to make objects travel faster than the speed of sound, i.e., the Mach number. Ernst Mach predicted that a conical shock wave trails behind objects traveling faster than the speed of sound. In terms of measurement, Mach 1 is the speed of an airplane flying through air equal to the speed of sound at that location. The importance of the Mach number has to do with a comparison of the inertial resistance to the compressional resistance of an object moving through fluid. Someone would have to invent the Reynolds number if man ever wanted to travel to outer space or cross-continents faster than the speed of sound.

These principles were used in analyzing the 2003 explosion of Space Shuttle Columbia. A fist-size hole opened in the fuselage after a heat tile tore away; gas, air, and speed mixed destroying the shuttle. A NASA model of the shuttle "flew" in a wind tunnel creating Reynolds numbers to identify the influence of certain conditions on the shuttle to learn how to avoid them in future flights. More than a decade later, the U.S. Naval Research Laboratory is using the Reynolds number to measure viscous flow through nozzles in advanced spacecraft propulsion systems. The objective is to improve the efficiency and safety of launching cube satellites in space already numbering in the hundreds from industry, academia, and government. Nearly three dozen satellites are being sent spaceward from a single launch, and the press is on to lower costs of launches even more.

The answer to why one paper airplane does not lift, float, and travel the distance of another paper airplane can be found by applying the Reynolds number. The Re affects the combinations of wings, tails, and fuselages. The paper airplane takes off with laminar flow of air. Viscosity is greater; there is greater drag and difficulty in lifting. There are ways to make the paper airplane more efficient per Re: short wings are better in launch, long wings enhance glide, and trim wings make a better launch because they are necessary for high lift in the glide pattern. Thick paper enhances the launch, but thin paper makes the paper plane lighter and is best for gliding.

Bibliography

Arnold, Jim, et al. "A Look Back at Ames’ Contributions to the Shuttle." NASA. Humans in Space. Nasa.gov, 29 March 2008. Web. 9 June 2016.

Blackburn, Ken. Ken Blackburn’s Paper Airplanes. Ken Blackburn’s Paper Airplanes, 2008. Web. 9 June 2016.

Crowie, J.M.G., and Valeria Arrighi. Polymers: Chemistry and Physics of Modern Materials.3rd. ed. Boca Raton: CRC Press, 2008. Print.

Osborn, Michael, et al. "Overcoming Low Nozzle Efficiency: A Test-Correlated Numerical Investigation of Low Reynolds Number Micro-Nozzle Flow." ARC Aerospace Research Central. American Institute of Aeronautics and Astronautics, 2015. Web. 9 June 2016.

"Reynolds Experiment." The Constructor - Civil Engineering Home. The Constructor - Civil Engineering Home, 2015. Web. 9 June 2016.

"Reynolds Number." You Tube. You Tube.com, 8 Dec. 2012. Web. 9 June 2016.

Editors of Encyclopaedia Britannica. "Reynolds number: Physics." Encyclopaedia Britannica. Encyclopaedia Britannica, Inc., 2016. Web. 9 June 2016.

Wilk, Stephen R. How the Ray Gun Got Its Zap: Odd Excursions Into Optics. Oxford: Oxford University Press, 2013. Print