The Physics of Swimming in Syrup

posted: 04/11/12
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In the 2008 Summer Olympics in Beijing, Michael Phelps exemplified athletic perfection in the pool. If he were forced to compete in a vat of pancake syrup, his swimming technique would suffer at first in the sticky substance. But in keeping with the principles of fluid mechanics, Phelps should be able to swim through it eventually at about the same speed as water.

How is that so? Read on to find out.

Viscosity, Einstein and Newton

If you placed one hand in a gallon of water and the other in a gallon of syrup, you'd immediately notice a difference in the liquids' viscosity, or thickness. Viscosity is the resistance of a fluid to change shape when an external force moves through it. It also measures stickiness, or how strongly a top layer of the fluid, known as the boundary layer, clings to the surface of a foreign object.

According to Einstein's viscosity equation, a fluid's thickness isn't always uniform. Water, for instance, is classified as a Newtonian fluid, meaning its viscosity is stable when temperature and pressure are constant. Non-Newtonian fluids, like syrup, contain polymer chains of macromolecules and are much less predictable. Their viscosity depends on shear rate, or the rate of movement between the liquid's layers. When the shear rate increases with turbulence, the behavior of the polymer chains varies depending on their properties and causes shear thickening or thinning.

Einstein's equation implies that swimming through non-Newtonian syrup is a gamble. But viscosity also has theoretical advantages.

What a Drag!

Hold your hand out of a car window while cruising down the highway, and you can feel wind drag push your palm backward. Drag works in opposition to inertia, or the natural tendency of an object to stay at rest or in motion (see Newton's first law).

In a swimming pool, drag is the cumulative horizontal resistance determined by our body size, speed and fluid viscosity. Friction between layers of fluid, called streamlines, produces viscous drag. The greater the viscosity of the liquid, the greater the frictional drag against our intended direction. In accordance with Newton's third law of motion, we also benefit from frictional force since it generates an equal and opposite reaction, or propulsion.

Reynolds Number

The act of swimming and forcefully displacing fluids out of our path creates turbulence beyond the boundary layer that clings to our bodies. Conversely, when streamlines glide across objects smoothly, it's referred to as laminar flow. Reynolds number is a measure of turbulence versus laminar flow. This ratio of inertia to viscosity explains theoretically how Phelps could swim through syrup without hurting his time -- as well as the limits of the mechanical phenomenon.

The key is body size. Inertia is calculated from speed, body size and fluid density. Humans' large mass can minimize the effect of, say, doubling the viscosity of water and maintain a high Reynolds number. Pancake syrup is about 2,500 times more viscous than water, but Phelps could utilize the added propulsion from thicker liquid to compensate. Drop a beetle in the same liquid, the Reynolds number would drop, and the tiny bug would have a much harder time navigating.

However, a vat of dark molasses with twice the viscosity of pancake syrup would probably prove impassable. Even fluid mechanics -- and Michael Phelps -- have their limits.

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