Practical Engineering
Applying theoretical mathematics to real-world engineering challenges.
The Colebrook-White Equation
The Colebrook-White equation is a pivotal mathematical formula in fluid dynamics facilitating the calculation of the Darcy friction factor. Developed by Cyril Frank Colebrook and Charles Metcalf White in 1937, this equation revolutionized the field of hydraulic engineering.
While numerical solutions and approximations have been developed to simplify calculation, the Colebrook-White equation cannot be solved explicitly for the friction factor, f. It requires iterative solving — a perfect use case for selectNsolve Basic™.
Colebrook-White Equation
Supporting Equations
The Reynolds number and Darcy-Weisbach head loss equation work together with Colebrook-White:
Reynolds Number
Darcy-Weisbach Head Loss
Iterative Solving Process
Because appears on both sides of the equation, a numerical solver must iterate until convergence. selectNsolve Basic™ handles this automatically:
Typical convergence achieved in 4–10 iterations — selectNsolve™ handles this in one click.
Colebrook-White equation solved using selectNsolve Basic™
Optimization
By modeling equations like Colebrook-White in Google Sheets™ using selectNsolve™, engineers can instantly evaluate how changes in pipe diameter (), roughness (), or Reynolds number () affect the friction factor. This turns a tedious iterative hand-calculation into an interactive design tool.
Optimization in action with selectNsolve Basic™