Chapter 7, Problem 7.9P

Interpretation Introduction

Interpretation: The percentage change in volumetric flow rate of water has to be determined at 2 different temperatures.

Concept introduction The Hagen Poiseuille equation also called the Hagen Poiseuille flow model relates the volumetric flow rate to the viscosity as follows,

  $\text{Q}\text{α}\frac{\text{1}}{\text{μ}}\mathrm{.......}\text{(1)}$

In this relation, the notations used are,

Q is the volumetric flow rate of the given fluid

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

The percentage change in the volumetric flow rate is given as,

  $\begin{array}{l}\text{\%}\text{change}\text{=}\left(\frac{{\text{Q}}_{\text{2}}\text{-}{\text{Q}}_{\text{1}}}{{\text{Q}}_{\text{1}}}\right)\text{×100}\\ \text{\%}\text{change}\text{=}\left(\frac{{\text{Q}}_{\text{2}}}{{\text{Q}}_{\text{1}}}\text{-1}\right)\text{×100 }\mathrm{.......}\text{ (2)}\\ \text{Substitute equation (1) in equation}\text{(2),}\\ \text{\%}\text{change}\text{=}\left(\frac{{\text{μ}}_{\text{1}}}{{\text{μ}}_{\text{2}}}\text{-1}\right)\text{×100}\mathrm{.......}\text{(3)}\end{array}$

  Q₁ is the flow rate of fluid at 32 $\text{°F}$

  Q₂ is the flow rate of fluid at 140 $\text{°F}$

  ${\text{μ}}_{\text{1}}$ is the viscosity of fluid at 32 $\text{°F}$

  ${\text{μ}}_{\text{2}}$ is the viscosity of fluid at 140 $\text{°F}$