Chapter 5, Problem 5.17P

Interpretation Introduction

Interpretation: The amount of polyethylene oxide to be added to water to increase its flow rate is to be calculated.

Concept introduction: Friction factor commonly known as the fanning friction factor is a measure in turbulent flow and is the ratio of shear stress to the product of the density and velocity head. It is given as,

  $\text{f}\text{=}\frac{\text{τ}}{\frac{\text{1}}{\text{2}}{\text{ρV}}^{\text{2}}}$

In the above formula, the notations used are,

  $\begin{array}{l}\text{f}\text{=}\text{Fanning}\text{friction factor}\\ \text{τ}\text{=}\text{Shear stress}\\ \text{ρ}\text{=}\text{Density of fluid}\\ \text{V = Velocity of fluid}\end{array}$

The above formula can be written as,

  $\text{f}\text{=}\frac{\text{ZD}}{{\text{2LV}}^{\text{2}}}\mathrm{.......}\text{(1)}$

Z is the total head developed

L is the length of the tube

D is the diameter of the tube

The Reynolds number for the fluid is given as,

  $\text{Re}\text{=}\frac{\text{ρVD}}{\text{μ}}\mathrm{.......}\text{(2)}$

  $\text{μ}\text{is the viscosity of fluid}$