Colebrook-White Pipe Flow Calculator
The Colebrook-White equation is an implicit formula used to calculate the Darcy-Weisbach friction factor for turbulent flow in a pipe. Here’s a concise table summarizing key aspects related to the Colebrook-White equation and its application in pipe flow:
| Aspect | Details |
|---|---|
| Equation | 1f=−2log10(ϵ/D3.7+5.74Re0.9)\frac{1}{\sqrt{f}} = -2 \log_{10} \left( \frac{\epsilon/D}{3.7} + \frac{5.74}{Re^{0.9}} \right)f1=−2log10(3.7ϵ/D+Re0.95.74) |
| Variables | – fff: Darcy-Weisbach friction factor |
| – ϵ\epsilonϵ: Pipe roughness height (m) | |
| – DDD: Pipe diameter (m) | |
| – ReReRe: Reynolds number | |
| Flow Regime | Applicable for turbulent flow (Re>4000Re > 4000Re>4000) |
| Roughness Values | Common values for different materials (approximate): |
| – Commercial steel: 0.045 mm | |
| – PVC: 0.0015 mm | |
| – Copper: 0.0005 mm | |
| Reynolds Number Calculation | Re=ρvDμRe = \frac{\rho v D}{\mu}Re=μρvD |
| – ρ\rhoρ: Fluid density (kg/m³) | |
| – vvv: Flow velocity (m/s) | |
| – μ\muμ: Dynamic viscosity (Pa·s) | |
| Solving the Equation | Iterative methods or numerical techniques (e.g., Newton-Raphson) are used due to its implicit nature. |
| Applications | – Pipeline design and analysis |
| – HVAC systems | |
| – Water supply systems | |
| – Chemical processing | |
| Limitations | – Not valid for laminar flow (Re<2000Re < 2000Re<2000) |
| – Assumes fully developed flow | |
| – Sensitivity to roughness and flow conditions |
This table provides a comprehensive overview of the Colebrook-White equation, its application, and relevant parameters. If you have any specific areas you would like to delve deeper into, feel free to ask!