Facts of the Matter: Many variables influence the flow of fluids

Werner Heisenberg, who revolutionized quantum theory with his famous uncertainty principle, said, “When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first.”

Laminar and turbulent flow regimes are two broad classifications that are important in the behavior of any system of moving fluids. The flow regime affects the amount of fluid friction, which determines the amount of energy required to maintain a level of flow and affects the heat transfer properties of the fluid.

Laminar flow is a semi- organized state where the fluid moves in parallel layers at different speeds with little or no vertical mixing, whereas turbulent flow is chaotic with much mixing throughout the fluid.

At low velocities flow is laminar, and at high velocities flow is turbulent. What makes fluid dynamics both complicated and interesting is that what qualifies as high or low velocity is different in different fluids and under different conditions.

Molecules in a stream of moving fluid interact at its edges and form a thin boundary layer. This layer changes the shape of the boundary ever so slightly, but enough that the boundary layer could separate from the boundary and create a shape that is much different from the boundary itself.

The flow conditions in and near the boundary layer are unsteady and constantly changing, but conjointly the size and shape of the boundary layer determine the strength of the forces that operate at the boundary. This nonlinearity creates a conundrum for physicists.

An empirical formula generates the Reynolds number, which represents the ratio of inertial forces to viscous forces in the fluid. The calculation of the Reynolds number differs for different situations. It depends on the size, shape and texture of pipes, channels or other surfaces and the speed, density and viscosity of the fluid.

It is named after Osborne Reynolds (1842-1912), who discovered that experimental results with wind tunnel models are invalid if the conditions used for experiments are the same as a full-size aircraft would encounter under actual conditions.

At high Reynolds numbers inertial forces dominate over viscous forces, and the flow is turbulent. At low Reynolds numbers viscous forces dominate over inertial forces, and the flow is laminar. There is a transition range where the flow is in a state that is neither purely laminar nor purely turbulent.

The problem is that there is no theorem relating Rey­n-olds number to turbulence, and there is no way to predict at what point within the transition range the transformation from laminar to turbulent will take place.

Despite the ubiquitous role that flow regime plays in multiple aspects of our lives, we still do not know what happens within the fluid to initiate the transformation. It appears to lie in that mysterious and growing field of mathematical chaos along with weather and population ecology.

This is inconvenient when it is an engineering problem such as a distribution system for water, or a heat exchange system in a power plant. But when it involves the flow of air over the wing of an airplane, it is downright critical since a laminar boundary layer at the wing surface provides lift while turbulence creates drag.

Richard Brill is a retired professor of science at Honolulu Community College. His column runs on the first and third Fridays of the month. Email questions and comments to brill@hawaii.edu.