Viscous Flow in Pipes.pdf

Appendix: Derivation of the law of the wallFor the sublayer, Prandtl suggested in 1930 that u beindependent of sublayer thickness, andu = f( μ, τ , ρ, y)wUsing the pi method:a b c1 1Π1= uμτwρ→ a= 0, b=− , c=2 2d e f1 1Π2= yμτwρ→ d =− 1, e= , c=2 2⇒Π = u/ τ / ρ = u/ u*, where τ / ρ ≡u*1ywyu*νΠ2= τw/ ρ =νu ⎛ yu*⎞→ = f ⎜ ⎟u * ⎝ ν ⎠u yu*Experimentally, it is found that = .u * νw