Chapter 2, Problem 2.10P

Interpretation Introduction

Interpretation: The volume fraction and weight fraction of the sand in a suspension of very fine sand particles in water is to be calculated.

Concept introduction: The volume fraction of a substance is the volume of the given substance to the total volume of the substances present in the suspension. It can be related with a density as,

  ${\text{ρ}}_1\text{Vx}\text{+}{\text{ρ}}_2\text{V(1-x)}\text{=}\text{ρV}\mathrm{......}\text{(1)}$

  $\begin{array}{l}{\text{ρ}}_1\text{=}\text{Density}\text{of}\text{sand}\\ {\text{ρ}}_2\text{=}\text{Density}\text{of}\text{water}\\ \text{x}\text{=}\text{Volume}\text{fraction}\text{of}\text{sand}\\ \text{V}\text{=}\text{Total}\text{volume}\text{of}\text{suspension}\end{array}$

The weight fraction of the sand is the ratio of the weight of the sand to the total weight of the suspension. It is given as,

  $\begin{array}{l}\text{y}\text{=}\frac{{\text{W}}_{\text{1}}}{\text{W}}\mathrm{......}\text{(2)}\\ \text{y}\text{=}\text{Weight}\text{fraction}\text{of}\text{sand}\\ {\text{W}}_{\text{1}}\text{=}\text{Weight}\text{of}\text{sand}\\ \text{W}\text{=}\text{Weight}\text{of}\text{suspension}\end{array}$