Handbook of Civil Engineering Calculations

The actual power output from a hydro station is P = HQwe/550, where P = horse-
power output; H = head across turbine, ft; Q = water flow rate, ft^3 /s; w = weight of wa-
ter, lb/ft^3 ; e = turbine efficiency. Substituting in this equation for the plant shown in Fig.
I6b, for flow rates of 500 and 1500 m^3 /s, we see that a tripling of the water flow rate
increases the power output by only 38.7 percent, while the absolute head drops 53.8 per-
cent (from 3.9 to 1.8 m). This is why the tail-water level is so important in small hydro
installations.
Figure \6c shows how station costs can rise as head decreases. These costs were esti-
mated by the Department of Energy (DOE) for a number of small hydro power installa-
tions. Figure 16 shows that station cost is more sensitive to head than to power capacity,
according to DOE estimates. And the prohibitive costs for developing a completely new
small hydro site mean that nearly all work will be at existing dams. Hence, any water ex-
ploitation for power must not encroach seriously on present customs, rights, and usages of
the water. This holds for both upstream and downstream conditions.

3. Outline machinery choice considerations
   Small-turbine manufacturers, heeding the new needs, are producing a good range of semi-

Power, KW Head, ft

(d) (c)

FIGURE 16. (a) Rising tail-water level in small hydro projects can seriously curtail po-

tential, (b) Anderson-Cottonwood dam head dwindles after a peak at low flow, (c) Low

heads drive DOE estimates up. (d) Linear regression curves represent DOE estimates of

costs of small sites. (Power.)

Structural

Equipment

Total site

costs

•Administrative,

engineering, other

Head, m

Flow, m^3 /s

Structural

Equipment

Administrative,

engineering, other

Flow

(b)

Flow

Gross

head

Tail

water

level

Costs, $/kW

Available

head,

m

Costs,

$/kW