Chapter 3, Problem 3.2P

Interpretation Introduction

Interpretation: Reynolds number for transition to turbulent flow is based on the thickness of the laminar boundary layer $\left(Z_x\right)$ on a flat plate instead of $x$ which is close to the transition Reynolds number for flow in a pipe should be proved.

Concept introduction: The Reynolds number based on the thickness of the boundary layer is given as,

  ${\text{N}}_{\mathrm{Re}{Z}_x}=\frac{\rho u_{\infty }{Z}_x}{\mu }$

The given value of boundary layer thickness is,

  $Z_x=5.5{\left[\frac{\mu x}{\rho v\infty }\right]}^{1/2}$

Plugin the given value of boundary layer thickness in the above expression as follows:

  ${\text{N}}_{\mathrm{Re}{Z}_x}=\frac{\rho u_{\infty }5.5{\left[\frac{\mu x}{\rho v\infty }\right]}^{1/2}}{\mu }$