Chapter 5, Problem 5.8P

Interpretation Introduction

Interpretation: The change in pressure drop for the same flow rate and change in flow rate for the same pressure drop is to be determined.

Concept introduction: The change in pressure across a pipe due to smoothness or roughness is known as the pressure drop. The pressure drop for any type of flow is given as,

  $\text{ΔP}\text{=}\frac{{\text{2fρL<mover accent="true"><mo> v </mo><mo>¯</mo></mover>}}^{\text{2}}}{\text{D}}$ .......... (1)

The notations used here are,

  $\text{ρ}$ = Density of the fluid

f = Fanning Friction factor

L = Length of the pipe

D = Diameter of the pipe

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

The Reynolds number is given as,

  $\text{Re = }\frac{\text{ρ<mover accent="true"><mo> v </mo><mo>¯</mo></mover> D}}{\text{μ}}$ .......... (2)

The notations used here are,

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

D = Diameter of pipe

  $\text{μ}$ = Viscosity of the fluid

  $\text{ρ}$ = Density of fluid

The flow rate of the fluid is given as,

  $\text{Q}\text{=}\text{A<mover accent="true"><mo> v </mo><mo>¯</mo></mover>}$ .......... (3)

A = Area of the pipe

  $\text{A}=0.25{\text{πD}}^2$ .......... (4)

The roughness parameter is given as, $\frac{\text{k}}{\text{D}}$ where k is roughness of the pipe. It shows how much friction is present in the pipe and with the help of the roughness parameter, f can be calculated from the friction factor chart.