Chapter 4, Problem 4.12P

Interpretation Introduction

Interpretation:

The value of average velocity in pipe in terms of maximum velocity for the given conditions should be determined.

Concept introduction:

For the flow in a pipe, generally the velocity distribution are parabolic in nature as shown in figure,

  

The velocity is maximum at the center and the ratio of maximum velocity to average velocity is equal to 2 given by the below relationship,

  $\frac{{\text{v}}_{\text{max}}}{{\text{v}}_{\text{average}}}=2$

The formula for maximum velocity is given as,

  ${\text{v}}_{\max }=\frac{-1}{4\mu }\frac{\partial P}{\partial x}{R}^2$

The relationship of average velocity of flow in a pipe,

  $v_{average}=\frac{1}{\text{A}}{\displaystyle \underset{\text{A}}{\int }\text{udA}}$

Where,

  $v_{average}$ is the average velocity of pipe.

A is the cross-section area of the pipe.

dA is the cross-section area of small section.

u is the velocity variation.