The fundamental assumption of boundary-layer theory is that the layer is thin compared to other length scales such as the length or radius of curvature of the surface on which the boundary layer develops

According to the boundary-layer theory, when a fluid flows past an object, frictional effects are significant only in a thin region close to the wall, where large transverse gradients of velocity exist. Within this thin boundary layer, the velocity rises rapidly from zero at the wall to the freestream value at its edge

Across this thin layer, which can exist only in high Reynolds number flows, the velocity varies rapidly enough for viscous effects to be important

However, thin viscous layers exist not only next to solid walls but also in the form of jets, wakes, and shear layers if the Reynolds number is sufficiently high. So, to be specific, we shall first consider the boundary layer contiguous to a solid surface, adopting a curving coordinate system that conforms to the surface where x increases along the surface and y increases normal to it