Chapter 5, Problem 5.22P

(a)

Interpretation Introduction

Interpretation:

The pressure drop per unit length is to be calculated.

Concept Introduction :

The Reynolds number is to becalculated to calculate the friction factor.

The Reynolds number is,

  $N_{\mathrm{Re}}=\frac{\rho VD}{\mu }$

The formula for calculating the pressure drop per unit length is,

  $\frac{\Delta P}{L}=\frac{2f\rho V^2}{D}$

(b)

Interpretation Introduction

Interpretation:

The thickness of the viscous sub layer and that of the buffer layer is to be calculated.

Concept Introduction :

The thickness of the viscous sub layer and the buffer layer is calculated with the help of velocity distribution for the turbulent flow.

The formula for calculating the thickness of the different layer is,

  $y^{+}\equiv \frac{y{u}^{\ast }\rho }{\mu }$

The formula for calculating the frictional velocity is,

  $u^{\ast }=\overline{V}\sqrt{\frac{f}{2}}$

(c)

Interpretation Introduction

Interpretation:

The fraction of the total flow in viscous sub layer and in buffer layer is to be calculated.

Concept Introduction :

The universal velocity-distribution equations are used to calculate the fraction of the total flow in these layers.

The formula for calculating the fraction of the total flow in these layers is,

  $\frac{sublayerflow}{total}=\frac{u}{V}\times \frac{4Dy}{D^2}$

  $\frac{bufferlayerflow}{toatlflow}=\frac{u}{V}\times \frac{S_b}{D^2}$