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 shear force per unit volume in the \(x\) direction. Locate the maximum shear force per unit volume; interpret this result.

Data From Problem 5.10

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5.10 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 freestream velocity, U, at the bound- ary-layer edge (y = 8). The equation for the profile is u=Uy/8, where 8=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 8=5 mm.