When water flows from a reservoir to a turbine and from a turbine to the tailwater, it loses head through boundary friction (from the interior surfaces of the water conveyance) and form friction (internal friction in the water caused by changes in the shape of the flow boundary.) Form friction is also called “minor losses”, although they are sometimes relatively large. Head loss is measured in metres (m). The total head loss is the sum of the friction and form loss in each component of the water conveyance.
Boundary friction is typically calculated by the Darcy-Weisbach equation, which relates friction head loss (h) to a friction factor (f), length of the water passage (L), velocity of flow (v), gravitational acceleration, g and the hydraulic radius of the conveyance section (R) as follows:
h = (f . L . v²) / (2 . g . R) (Darcy-Weisbach)
The hydraulic radius is the ratio of the cross sectional area of the water conveyance, A, and the perimeter, p. Thus:
R = A / p
The most common minor losses are as follows:
- intake loss
- transition loss where the conveyance expands, contracts or changes shape
- bend losses
- valve losses and
- exit losses
The head loss in each part of the water conveyance is proportional to the square of the velocity (v²) in that part of the water conveyance.
The total head loss for the water conveyance is proportional to the square of the flow rate (Q²).