For flow over a flat plate with an extremely rough surface, convection heat transfer effects are known to be correlated by the Nμ x= 0.04 Rex^0.9 Pr^1/3

For airflow (v =15.89x10^-6m² /s, Pr=0.71 and density 1.16kg/m^3) at 50 m/s, what is the surface shear stress at x =1m from the leading edge of the plate?

the surface shear stress at x =1m from the leading edge of the plate is 4.1973 N/m²

Explanation:

Given that;

density s = 1.16 kg/m³

velocity = u = 50 m/s

kinetic viscosity r = 15.89 × 10⁻⁶ m²/s

xL = 1m from the leading edge of the plate

Now Reynold number (Rex)

Rex = UxL / r

Rex = (50 m/s × 1m ) / 15.89 × 10⁻⁶ m²/s

Rex = 3146633.1025

since Rex is greater than 5×10⁵ { Turbulent flow }

so Local skin friction coefficient

⇒ Cfx = 0.0577 / (Rex)^1/5

Cfx = 0.0577 / (3146633.1025)^1/5

Cfx = 0.0028947

Now Shear stress (y)

y = Cfx × 1/2 × su²

y = 0.0028947 × 1/2 × 1.16 × (50)²

y = 4.1973 N/m²

∴ the surface shear stress at x =1m from the leading edge of the plate is 4.1973 N/m²

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