7.4 Problems

Problem 7.1 The flow past a flat plate has a unit Reynolds number Re ^u _? = 10 ⁶ m ^?1. Assume incompressible flow and determine on the plate at x = 1.0 m for a) laminar and b) turbulent flow the boundary-layer thicknesses ?, ? ₁, ? ₂, the shape factors H ₁₂, and for turbulent flow in addition S _us, and ? _sc.

Solution: a) ? = 0.005 m, ? ₁ = 0.00172 m, ? ₂ = 0.00066 m, H ₁₂ = 2.591. b) ? = 0.0233 m, ? ₁ = 0.00292 m, ? ₂ = 0.00271 m, H ₁₂ = 1.286, ? _{? s} = 0.000116 m, ? _sc = 0.000535 m.

Problem 7.2 The flow past a flat plate is that of Problem 7.1. Assume incompressible flow and determine on the plate, but now at x = 10.0 m for a) laminar and b) turbulent flow the boundary-layer thicknesses ?, ? ₁, ? ₂ the shape factors H ₁₂, and for turbulent flow in addition ? _us, and ? _sc.

Problem 7.3 Compare and discuss the results from Problem 7.1 and 7.2 in view of Table 7.3. Program the equations for the thicknesses and plot them as functions of x in the interval 0.0