Chapter 5, Problem 5.3P

Interpretation Introduction

Interpretation: The relationship between the local and maximum velocity of a Newtonian fluid in the Laminar flow in a rectangular channel is to be derived along with ratio of maximum and average velocity.

Concept introduction: The flow in a liquid is said to be Laminar when the Reynolds number is less than 2100. The equation for laminar flow can be derived by the force balance between the channel. The equation for the shear stress is a very useful measure here as it can help in achieving the final result. The shear stress equation is,

  $\text{τ}\text{=}\text{-μ}\frac{\text{du}}{\text{dy}}\mathrm{.......}\text{(1)}$

The notations used here are,

  $\begin{array}{l}\text{τ}\text{=}\text{Shear stress}\\ \text{μ}\text{=}\text{Fluid viscosity}\\ \frac{\text{du}}{\text{dy}}\text{=}\text{Strain}\text{rate}\end{array}$

The maximum velocity is obtained at the center of the rectangular channel and local velocity is the velocity at any point in the channel.