Chapter 8, Problem 8.15P

Interpretation Introduction

Interpretation: The velocity distribution around a vertical rod for the fully developed flow is to be determined.

Concept introduction:

The differential equation governing the motion of the fluid at some distance from the vertical rod is,

  $\frac{\text{1}}{\text{r}}\frac{\text{d(rτ)}}{\text{dr}}\text{+}\text{ρg}\text{=}\text{0}$ ....... (1)

  $\text{τ}$ = Shear stress developed

  $\text{ρ}$ = Density of the fluid

g = Acceleration due to gravity

r = Distance on the rod at a point

The shear stress developed is given as,

  $\text{τ}\text{=}\text{μ}\frac{\text{dv}}{\text{dr}}$ ....... (2)

  $\text{μ}$ = Viscosity of the fluid

  $\frac{\text{dv}}{\text{dr}}$ = Shear rate

Here, v is the velocity in vertical direction