POWER GENERATION AND TRANSMISSION 73
of various small transverse sections of definite area, running from surface to bed of the stream. Discharge is expressed in cubic feet per second. It usually varies more rapidly than the transverse area of the stream: high water increasing the discharge more than it does the area. A plot of discharge against relative surface level permits of quick estimates of variations in discharge.
While large discharges are accompanied by high surface levels above the dam, the transverse area of the stream below the dam is generally so contracted that large discharges increase the tail water level more than they do the head water level. The available head is the difference of head between head water and tail water. Hence head decreases as flow increases, and the adaptability and capacity of the wheels for varying heads and flows must be considered.
The hydrograph, or plot of discharge against time, and the power curve, or plot of discharge X head against time, show the fluctuations in flow and power over a period of months or years, and determine what flow or power may be relied on as fixing the desirable capacity of installation. The mass-flow curve plots flow against time cumulatively. A tangent drawn to the lowest point of this curve from the origin shows the average flow which may be depended on with unlimited storage of water. The possibility of storage depends largely on whether there are rights ^ below the site of power development in ~o
question which make interference with I-----------------------------------
the natural stream flow unlawful. In Annual Load,hp.-hrs.
any case, storage can scarcely be con- FIG. 35.—Load-plant cost curves,
sidered except where the topography of the country favors it: i.e., in high-head plants. Pondage (moderate storage, of a few hours' discharge only) may be used even in low-head plants where the load for short periods during a day exceeds that corresponding with the flow: but even pondage is impossible if the stream flow must be left unimpaired.
A really valuable hydrograph or mass-flow curve requires observations extending over several years, and these are not always available. A rough estimate of flow variations may then be obtained from rainfall records. If the monthly rainfall over the known drainage area of the stream has been recorded, the maximum possible monthly stream flow is the product of the rainfall in feet by the drainage area in square feet. This value will be most closely approximated in a wooded rocky country where practically all rainfall is carried off by streams. In other instances as in sandy deserts the rainfall may practically all percolate into the soil or be lost by evaporation, so that the probable ratio of run-off to rainfall must be carefully estimated for the plant in question, by considering the nature of the soil and vegetation, humidity, etc.
Cost of Development and Generation.—A waterpower project may include dams, power-house buildings, head race or penstock, tail race, gates and sometimes pondage or storage. Approximately $100 per horsepower for low-head plants without storage arid twice this or more for high head plants including storage may be counted on. Waterpower plants are in general the most expensive of all types to install and the least expensive to operate: the cost of power per horse-power-year ranging from 110 to $35. As with all power plants, total cost per year tends to vary linearly with the annual-output: i.e., a good load factor lowers the cost per horsepower. The curves of the accompanying diagram are typical. The intercepts on the vertical axis are proportional to the relative