Ludwig Prandtl fluid dynamics |

## Boundary layer

Calculations of the dynamics of fluids require values for the pressure on the fluid, and its inertia, velocity, density, and viscosity. Ludwig Prandtl simplified calculations of aerodynamic flow by dividing a flow over a bounding surface into two areas, the first inside a boundary layer near the surface, where the flow is affected by viscosity, and the second outside the boundary layer, where the effects of viscosity can be ignored.

## Boundary layers

Heat transferring from a surface also has a boundary layer. Design of airplanes, ships, submarines, and offshore drilling platforms. The blades of the Tesla turbines and pumps. Oscillating objects and rotating fluids. produce laminar or turbulent flows and all have boundary layers.

## Boundary definition

The line where the speed of a flow
is slowed by the drag on a surface
exactly one percent.
The 49^{th} parallel north.
Where it was in my grandfather’s day.
In this business,
one can sometimes choose any number
as long as it’s always the same number.
Especially, of course,
if it comfortably corresponds
to agreed-upon reality.

On interesting thing about mathematical discoveries is that the original problem over time becomes less important as new uses for it are developed. The problem with property boundaries is that their definitions are too often rooted in a history of exploitation and violence, not in the nature of the land. Gary Snyder has said that political boundaries should outline watersheds, but governments invested in their arbitrary borders should not be expected to agree.

See also in

The book of science:D’Alembert’s paradox—Jean le Rond d’AlembertReynolds number—George Gabriel StokesEkman transport—Vagn Walfrid Ekman, Fridtjof NansenTesla turbine—Nikola TeslaReadings on wikipedia: