Chain velocity to Reynolds to friction factor to drop: water at 1.27 m/s in DN100 gives Re 127000, f 0.0167, and 0.135 bar over 100 m.
The four-link chain
Velocity from Q/A feeds Re = rho v D / mu, which selects the friction law, which feeds dP = f(L/D)(rho v^2/2). Breaking the chain anywhere, for example guessing f, quietly invalidates the pump head.
Worked DN100 x 100 m
Water at 1.27 m/s in 100 mm gives Re 127000, turbulent. Blasius gives f 0.0167 and the 100 m run loses 0.135 bar (13499 Pa). Rerun with project roughness via Colebrook before detailed design.
Adding fittings and building the curve
Convert each fitting with its K or Le/D value, add to the straight-run drop, and fit H = H_static + kQ^2 through the duty point. That k is what the pump selection inherits.
Formulas
Reynolds
Re = rho v D / mu
Below ~2300 laminar, above ~4000 turbulent.
Darcy-Weisbach
dP = f(L/D)(rho v^2/2)
f from 64/Re, Blasius, or Colebrook.
Worked example
DN100 x 100 m water
Inputs: Re 127000; L 100; D 100; v 1.27.
Calculation: f 0.0167; drop 0.135 bar.
Frequently asked questions
How do I know the regime?
Re below ~2300 laminar, above ~4000 turbulent; between is transitional.
Blasius or Colebrook?
Blasius suits smooth turbulent screening; rough or large Re needs Colebrook/Moody.
How do I add fittings?
Use sum-K for a few fittings or Le/D to metres of straight pipe.
Sources and further verification
- Darcy-Weisbach equation — Wikipedia
- Moody chart — Wikipedia
Next step