Looking at Reynolds’ contributions from laminar calm to fully turbulent storm.

In a talk I gave a few years ago about secondary refrigerants, I spoke about five men whose work in fluid mechanics had transformed our ability to calculate fluid flow and heat transfer. They were Osborne Reynolds, Ludwig Prandtl, Wilhelm Nusselt, Thomas Stanton and Allan Colburn. If you have only come across one of them, then I am fairly sure it would be Professor Reynolds.

Reynolds was born in 1842 in Belfast, Ireland, but grew up in the southeast of England on the border of Essex and Suffolk. His father, also named Osborne, was a school headmaster and clergyman who had a love of mathematics and all things mechanical. Young Osborne inherited this enthusiasm and, as a teenager before going to university, he worked for two years as an apprentice in a rather unusual shipyard. The Watling Works in Stony Stratford, just north of Milton Keynes, was established by Edward Hayes around 1850 to manufacture lightweight but powerful steam engines for agricultural machinery. The Hayes engine was soon adapted for marine applications, initially to power canal boats, and then as that business grew, the firm diversified into building complete ships for river and coastal navigation, despite the fact that the yard was over seventy miles from the coast and the finished vessels had to be transported by road to a suitable launching point.

One of Edward Hayes’ innovations was to introduce a heat exchanger in the canal boats as a “surface condenser” with water flow induced by the pressure difference between the canal water at the side of the boat and in the eddy currents at the stern. Osborne Reynolds joined the firm just at the time that Hayes was starting his boat building enterprise, and the young man noted that a true understanding of the mechanical phenomena that he was seeing required a deeper understanding of mathematics, so after his apprenticeship he went to Queens College, Cambridge to take a degree in mathematics.

When he graduated in 1867, he worked for a short time in London as a civil engineering consultant before his appointment in 1868 to the newly founded chair of Civil and Mechanical Engineering at Owens College, Manchester (now part of the University of Manchester) where he remained until his retirement in 1905.

Reynolds’ life’s work in Manchester was in the investigation and characterization of the ways in which liquids and gases flow. He realized that the distinction between laminar and turbulent flow was related to the relationship between the inertial forces on the fluid, which tend to keep it flowing in the same direction and the viscous forces, which tend to drag the flow into eddying patterns.

The inertial force is the cross sectional area of the flow multiplied by the density and the velocity squared (Fi = Aρv²), and the viscous force is the area of the flow multiplied by the velocity and the dynamic viscosity and divided by the diameter of the tube (Fv = Avμ/D). Reynolds showed that if this ratio Fi/Fv was less than about 2,000 then the flow would be “regular,” which he also called “streamlined” and which we now call laminar. If the ratio was more than about 3,000, the flow would be “sinuous” or “eddying,” which we now call turbulent. The lower and upper bounds of the transition region between the two types of flow are now taken to be 2,300 and 2,900.

The Reynolds number, as we now call it, is the density times the diameter times the velocity divided by the viscosity. It’s interesting to note that these four parameters fall into three distinct classes for any application. Density and viscosity are measures of what the fluid is, diameter is a measure of where the fluid is and velocity is a measure of how it’s behaving. It’s the combination of all three—what, where and how—that makes the Reynolds number so useful.

Reynolds said that his investigation was prompted by the observation that hot water tended to be more regular in flow than cold water, which was more sinuous, which made him wonder whether the difference in density was significant.

It’s not a question of regular flow being good and sinuous flow being bad: if you want to minimize pressure drop, for example in distribution pipes, then you want the flow to be laminar, so the Reynolds number should be less than 2,300. If, on the other hand, you wish to achieve maximum heat transfer to or from the fluid then turbulent flow ensures good mixing and good heat transfer, so the Reynolds number should be more than 2,900, but the price that has to be paid is an increase in pressure drop.