The drag on a body immersed in an oncoming flow is defined as the force on the body in a direction parallel to the flow direction. In a very slow-moving fluid the drag on a body may be directly attributable to the viscous, frictional shear stresses set up in the fluid due to the fact that, at the body wall, there is no relative motion. This type of flow is known as Stokes' flow after Sir George Stokes.
Two centuries before Stokes, Isaac Newton showed that that the shear stress t at a boundary wall, or between two layers of fluid moving relative to one another, is proportional to the transverse velocity gradient at the boundary, or between the two layers:
d y where the constant of proportionality is p the fluid viscosity.
Using Newton's theory, Stokes determined the drag force on a sphere in creeping flow (Figure A3.1).
where d is the sphere diameter and U is the general flow velocity.
The inviscid flow pattern around a cylinder (Figure A3.2) appears very similar to that of creeping flow but the nature of the flow is very different indeed. By definition inviscid flow causes no viscous drag but it also causes no pressure drag, that is, drag caused by pressure forces aggregated over the whole surface area. The pressure distribution for the inviscid flow past a cylinder is shown in Figure A3.3, where the atmospheric pressure has been subtracted from the pressure around the surface. The symmetry of the pressure distribution fore and aft shows clearly that no pressure drag arises. At the nose of the body the flow is brought exactly to rest and this is called the stagnation point. Another stagnation point occurs at the rear of the body.
In a real fluid, when the viscosity is low and the velocity is relatively high, the drag force that exists is due primarily to an asymmetric pressure distribution, fore and aft (Figure A3.5). This is caused by the fact that the fluid does not follow the boundary of the body but separates from it leaving low pressure, stagnant fluid in the wake (Figure A3.4). On the upstream side the flow remains attached and the pressure is high.
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