A linear velocity profile was used to model flow in a laminar incompressible boundary layer in Problem 5.10. Express the rotation of a fluid particle. Locate the maximum rate of rotation. Express the rate of angular deformation for a fluid particle. Locate the maximum rate of angular deformation. Express the rates of linear deformation for a fluid particle. Locate the maximum rates of linear deformation. Express the sheer force per unit volume in the x direction. Locate the maximum shear force per unit volume; interpret this result.
Problem 5.10 being referenced: A crude approximation for the x component of velocity in an incompressible laminar boundary layer is a linear variation from u = 0 at the surface (y = 0) to the free stream velocity, U, at the boundary-layer edge (y = ?). The equation for the profile is u = Uy/?, where ? = cx1/2 and c is a constant. Show that the simplest expression for the y component of velocity is v = uy/4x. Evaluate the maximum value of the ratio v/U, at a location where x = 0.5 m and ? = 5 mm.