Chapter 8, Problem 8.19P

Interpretation Introduction

Interpretation: The pressure drop of a Newtonian incompressible fluid in laminar flow is to be determined.

Concept introduction:

The Hagen-Poiseuille equation is used to determine the pressure drop in the Laminar flow region. The equation for the same is given as,

  $\frac{\text{ΔP}}{\text{L}}\text{=}\frac{\text{32μ<mover accent="true"> <mo>V</mo> <mo>¯</mo></mover>}}{{\text{D}}^{\text{2}}}$ ……. (1)

The notations used here are

  $\Delta \text{P}$ = Pressure drop in the pipe

L = Length of the pipe

D = Pipe diameter

  $\text{μ}$ = Fluid viscosity

  $\text{<mover accent="true"> <mo>V</mo> <mo>¯</mo></mover>}$ = Average velocity of the fluid

The average velocity of the fluid is given as,

  $\text{<mover accent="true"> <mo>V</mo> <mo>¯</mo></mover>}\text{=}\frac{\text{Q}}{\text{A}}$ ……. (2)

Q = Flow rate through the pipe

A = Area of the pipe

The area of the pipe is calculated as,

  $\text{A}\text{=}\frac{\text{π}}{\text{4}}{\text{D}}^{\text{2}}$ ……. (3)