Wednesday, November 3, 2010

Applications of Colebrook Equation

Applications of Colebrook Equation

Turbulent fluid flows in pipes, tubes and open channels play an important role in hydraulics, duct design, chemical engineering, and transportation of hydrocarbons,  for example. Fluid flows induce a significant loss of energy due to the dissipation due to turbulence and wall friction depending on the flow regime and the friction on the rigid boundaries. In this paper, we examine how exactly the Colebrook White equation is employed for calculations.
Flow Regimes:
The flow regimes 
  • Laminar flow
  • Transition between laminar and turbulent flow
  • Fully turbulent flow in smooth conduits
  • Fully turbulent flow in rough conduits 
  • Free surface flow
Fully turbulent flow in rough conduits
Most of the industrial applications (like transportation of fluids) requires moderate velocity and volume of flow rate. As the pipe used are kept moderately small diameters due to economy and space considerations, the industrial flow of liquid will be often in the turbulent regime. Air flow through exhaust ducts system should have sufficient velocity to capture and carry dust particles and thus the condition is turbulent.

Reynolds Number and Turbulent Flow
The Reynolds number expresses the ratio of inertial (resistant to change or motion) forces to viscous (heavy and gluey) forces. It is well known from experiments now that turbulent flow occurs at Re > 4000.
Re = V D / ν
V = velocity, D is diameter and ν is Kinematic Viscosity
Kinematic Viscosity  ν = μ / ρ
μ = viscosity and ρ = density
Colebrook Equation and Reynolds Number
As already stated, most of the industrial fluid flow will be in a regime Re > 4000 and thus, the Colebrook equation can be used to calculate friction factor f  for such applications.
    * f is the Darcy friction factor
    * Roughness height, e
    * Hydraulic diameter,d
    * Re is the Reynolds number.
Once friction factor f  is known, Darcy Weisbach equation can be easily used to calculate head loss
    * hf is the head loss due to friction;
    * L is the length of the pipe;
    * D is the hydraulic diameter of the pipe;
    * V is the average velocity of the fluid flow, = Q/A = volumetric flow rate Q per unit cross-sectional wetted area A;
    * g is the local acceleration due to gravity;
    * f is a dimensionless coefficient called the Darcy friction factor. It can be found from a Moody diagram or Colebrook equation.

Head Loss and Pressure Loss
    * the density of the fluid, r;
    * g is the local acceleration due to gravity
Power and Pressure Loss
Power wasted in pressure loss is given by following formula:
Pf  =  Q Dp/h
  • Pf , friction power loss in Watt
  • Q , flow rate in Cubic Meter /s
  •  Dp, friction loss in Pa
  • h is efficiency factor to account for the efficiency of the pump.

1) Anilkumar M, Optimum Pipe Sizing Fundamentals, Optimisations India, 2010 (In Press) Now availabe from AMAZON 
2) IRANIAN PETROLEUM STANDARDS IPS-E-PR- 440, Process Design of Piping Systems
3) Perry's Chemical Engineers Handbook, 8th Edition,