• Priyadarshini College of Engineering

• AE 502

Problem 1: (Problem 7.1 of Schetz) Air at standard temperature and pressure (STP) is flowing over a flat plate at 30 m/s. What is the value of Cf at x = 1.0 m? Calculate u∗. Solution: At STP, T = 20 ◦C and p = 1 atm, air has the following properties: ρ = 1.2 kg/m3 ν = 1.57 × 10−5 m2 /s The Reynolds number at a location of 1.0 m on the plate is given by, Rex = Ux ν = (30 m/s)(1.0 m) (1.57 × 10−5 m2/s) → Rex = 1, 910, 828 Assuming the critical Reynolds number for this flat plate is 500,000, then the boundary layer flow can be regarded as turbulent at a location of 1.0 m. The local skin friction law of Schoenherr can be used to estimate the skin friction over a smooth solid flat plate. This skin friction law takes the form, 1 p Cf = 4.15 log(RexCf ) + 1.7 Using a root finding scheme on a TI-89 calculator, the local skin friction for a Reynolds number of Rex = 1,910,828 yields, Cf = 0.00328 The value of u∗ at this location is given by, u∗ = Ue r Cf 2 = (30 m/s)r 0.00328 2 u∗ = 1.22 m/s 1 Problem 2: (Problem 7.2 of Schetz) For the flow in Problem 7.1, what is the thickness of the laminar sublayer? Estimate the distan