Fluid Dynamics

Even though Bernoulli's principle works extremely well in many cases, neglecting viscosity altogether often gives incorrect results. This is because even in fluids with very low viscosity, the fluid right next to the solid boundary sticks to the surface. This is known as the no-slip condition. Thus, however fast or easily the fluid away from the boundary may be moving, the fluid near the boundary has to slow down gradually and come to a complete stop exactly at the boundary. This is what causes drag on automobiles and airplanes in spite of the low viscosity of air.

The treatment of such flows was considerably simplified by the boundary layer concept introduced by Ludwig Prandtl (1875-1953) in 1904. According to Prandtl, the fluid slows down only in a thin layer next to the surface. This boundary layer starts forming at the beginning of the flow and slowly increases in thickness. It is laminar in the beginning but becomes turbulent after a point determined by the Reynolds number. Since the effect of viscosity is confined to the boundary layer, the fluid away from the boundary may be treated as ideal.