Air at 15C flows at 10 m/s over a flat plate of length 2 m. Using one-seventh power law of the turbulent flow, what is the ratio of local skin friction coefficient for the turbulent and laminar flow cases?

turbulent / laminar = Cft/Cfl = 6.23

or otherwise approximately, 6:1

Explanation:

First we calculate the Reynolds number, Re

Re = Vx/v

where V = velocity, x = L = length of flow of fluid, v = kinematic viscosity

since, the kinematic viscosity of air is 1.516 x 10^-5 m²/s

Re = (10m/s * 2m) / 1.516 x 10^-5 m²/s = 1.32x10^6

Obtained from seventh power law, the local skin friction coefficient, Cf

for laminar flow is

Cfl = 0.664 / Re½ = 0.664 / (1.32x10^6) ^1/2 = 0.664 / 1148.91 = 0.0005779

And for turbulent flow, Cft = 0.027/Re^1/7 = 0.027 / (1.32x10^6) ^1/7 = 0.027/7.49 = 0.0036

Hence, the ratio of the local skin friction for turbulent to laminar is

Ratio = turbulent / laminar = Cft/Cfl = 0.0036/0.0005779 = 6.23

or otherwise approximately, 6:1