Introduction to Fluid Mechanics

External Flow and Drag

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Often we do not need to know exactly what is going on in a fluid; we only need macroscopic measurements such as lift and drag. This clip focuses on drag and divides it conceptually into skin friction and form drag.

At very low Reynolds numbers, the inertial forces in a fluid tend to zero and the pressure forces are balanced by the viscous forces. For the flow around a sphere, there is an exact solution to the Navier-Stokes equation in this condition. It is known as Stokes flow. In this condition, all the drag is skin friction. As the Reynolds number increases, the form drag increases.

The strategies for reducing skin friction differ from those for reducing form drag. At high Reynolds numbers, where the drag on most bodies is dominated by form drag, it helps to streamline the downstream parts of bodies. This reduces the adverse pressure gradient and allows the boundary layer to remain attached.

If a velocity profile contains an inflection point (i.e. if the velocity gradient changes sign), then it will be convectively unstable, unless the Reynolds number is low. If a velocity profile contains two shear layers, as in the wake behind a bluff body, then it will be absolutely unstable, unless the Reynolds number is low. This absolute instability causes vortex shedding.

It is tempting to imagine that, as a fluid's viscosity tends to zero, its flow tends to the inviscid flow solution. This is not the case. The inviscid solution is singular. So why do we bother with inviscid flow? This clip explains why the concept of inviscid flow is useful, both conceptually and practically.

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