A model hull of length is towed at in water at ( , )

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluid Dynamics, Ch The boundary layer: Prandtl's equations and the Blasius solution

Problem

A model hull of length

L = 5.0\,\mathrm{m}

is towed at

U = 3.0\,\mathrm{m\,s^{-1}}

in water at

20^{\circ}\mathrm{C}

(

\rho = 998\,\mathrm{kg\,m^{-3}}

\mu = 1.00\times10^{-3}\,\mathrm{Pa\,s}

). Its skin friction only is to be estimated by treating the hull as a flat plate, as in Froude's method; wave-making resistance is set aside. Transition from laminar to turbulent flow occurs at

Re_x = 5\times10^{5}

. ((a)) Find the distance from the bow at which transition occurs. ((b)) Find

Re_L

for the whole hull. ((c)) Using

C_D = 1.328/\sqrt{Re_L}

for a fully laminar layer and

C_D = 0.074/Re_L^{1/5}

for a fully turbulent layer from the leading edge, compute both coefficients and compare them.

Browse the problem library