When a fluid flow approaches a flat solid surface as shown in Figure 5.54, the velocity of the fluid in contact with the solid surface must necessarily be equal to zero. In addition, the viscosity of...

When a fluid flow approaches a flat solid surface as shown in Figure 5.54, the velocity of the fluid in contact with the solid surface must necessarily be equal to zero. In addition, the viscosity of the fluid causes the velocity of the fluid away from the solid surface to be retarded. Retardation of the fluid is significant within a region called the boundary layer, which can be taken to have a thickness, δ, that depends on the distance, x, from the front of the solid surface. Observations indicate that the x-component of the velocity, u, can be expressed in normalized form by

where V is the free-stream velocity, y is the distance normal to the solid surface, and ν is the kinematic viscosity of the fluid. (a) Assuming that the fluid is incompressible, determine an expression for the normalized y component of the velocity, v/V , as a function of x, y, and δ. (b) Boundary layer analyses typically assume that v is negligible compared with u. Assess the justification of this assumption by finding the range of values of Re for which v/u ≤ 0.1 at the outer limit of the boundary layer.