Hydroelectric Power Generation - Renewable Energy: Technology, Economics and Environment - page 350

as constant, up and downstream of the intake structure. Therefore the losses
within the intake structure manifest as a decrease in the pressure level. They are
represented in Fig. 8.1 by the drop in the energy line at reference point 1.

2

v

p p Wa , 2

1

+ h =

2

+ h + ( + ξ ) (8.3)

1 2 IS

ρ g ρ g 2 g

Wa Wa

Penstock. The penstock bridges the distance between the headwater or intake
structure on one side with the turbine on the other (balance point 2 to balance
point 3; see Fig. 8.1). A further conversion of potential energy into pressure en-
ergy takes places. Because of the friction losses in the pipes, some of the energy is
lost. The Bernoulli Equation for the penstock can be written according to Equa-
tion (8.4).

2 2

v v

p p Wa , 2 Wa , 3

2

+ h + =

3

+ h + ( + ξ ) (8.4)

2 3 PS

ρ g 2 g ρ g 2 g

Wa Wa

The loss coefficient, ξ PS , of the penstock is a result of the friction factor and the
diameter of the penstock, and it increases proportionally to the length of the con-
duit. The friction factor is again dependent on the diameter, the flow velocity and
the surface roughness of the penstock; for practical utilisation it can be obtained
from relevant diagrams (e.g. /8-1/).
While the length of the penstock is dependent on the plant specifications, the
diameter can be varied. A diameter increase reduces the friction losses and the
turbine power increases. However, the penstock-related costs increase at the same
time. Therefore the aim is always to achieve a technical and economic optimum.
Run-of-river power stations with low heads do not have a penstock; the water
flows directly from the intake structure into the turbine.

Turbine. In the turbine, pressure energy is converted into mechanical energy (ref-
erence point 3 to reference point 4; see Fig. 8.1). The conversion losses are de-
scribed by the turbine efficiency η Turbine (Chapter 8.2.3). Equation (8.5) describes
that part of usable water power that can be converted into mechanical energy at
the turbine shaft P Turbine .

P = ηρ gq & h

(8.5)

Turbine Turbine Wa Wa util

h util is the usable head at the turbine, and the term ( ρ Wa g q . Wa h util ) represents the
actual usable water power P Wa,act .
Losses within the turbine are differentiated as volumetric losses, losses due to
turbulence, and friction losses. As a result of these losses the power at the turbine
shaft P Turbine in Equation (8.5) is less than the usable water power P Wa,act .