Hydropower
Penstock Friction Head Loss (Darcy-Weisbach)
h_f = f \times (L/D) \times (V^2 / 2g)
Variables
| hf | Friction head loss | m |
| f | Darcy friction factor | - |
| L | Penstock length | m |
| D | Penstock diameter | m |
| V | Flow velocity | m/s |
Engineering Example
A 500 m, 1.2 m diameter penstock at 4 m/s with f = 0.02: hf = 0.02×(500/1.2)×(4²/(2×9.81)) ≈ 6.8 m.
Practical Site Example
Checked during penstock diameter selection — too small a diameter wastes head to friction before it ever reaches the turbine.