then the velocity profile, defined as u(x,y) at x for all y, takes on a parabolic profile in the y-direction and the boundary layer thickness is just H/2. At the solid walls of the plate the fluid has zero velocity (no-slip boundary condition), but as you move away from the wall, the velocity of the flow increases without peaking, and then approaches a constant mean velocity ue(x). This asymptotic velocity may or may not change along the wall depending on the wall geometry. The point where the velocity profile essentially reaches the asymptotic velocity is the boundary layer thickness. The boundary layer thickness is depicted as the curved dashed line originating at the channel entrance in Figure 1. It is impossible to define an exact location at which the velocity profile reaches the asymptotic velocity. As a result, a number of boundary layer thickness parameters, generally denoted as , are used to describe characteristic thickness scales in the boundary layer region. Also of interest is the velocity profile shape which is useful in differentiating laminar from turbulent boundary layer flows. The profile shape refers to the y-behavior of the velocity profile as it transitions to ue(x). The 99% boundary layer thickness The boundary layer thickness, , is the distance normal to the wall to a point where the flow velocity has essentially reached the 'asymptotic' velocity, . Prior to the development of the Moment Method, the lack of an obvious method of defining the boundary layer thickness led much of the flow community in the later half of the 1900s to adopt the location , denoted as and given by as the boundary layer thickness. For laminar boundary layer flows along a flat plate channel that behave according to the Blasius solution conditions, the value is closely approximated by where is constant, and where is the Reynolds number, is the freestream velocity, is the asymptotic velocity, is the distance downstream from the start of the boundary layer, and is the kinematic viscosity. For turbulent boundary layers along a flat plate channel, the boundary layer thickness, , is given by This turbulent boundary layer thickness formula assumes 1) the flow is turbulent right from the start of the boundary layer and 2) the turbulent boundary layer behaves in a geometrically similar manner (i.e. the velocity profiles are geometrically similar along with the flow in the x-direction, differing only by scaling parameters