between the support and expansion joints, and longitudinal movements
over the supports due to temperature changes.
The energy of the flow through a penstock is inevitably reduced
owing to entry and friction losses. Although the friction losses can be mini-
mized by careful selection of the pipe diameter, and its entrance losses can
be minimized by a bell-mouthed entrance, an economical penstock dia-
meter may be determined from a study of the annual charges on the cost
of the installed pipe compared with the lost revenue due to this power loss.
As can be seen from Fig. 12.18, energy losses decrease with the increasing
diameters while construction costs increase. A diameter which minimizes
the total annual costs can be determined from the sum of the two costs.
Fahlbusch (1982) reformulated the objective of the economic analy-
sis in terms of the amount of the invested capital and the capitalized value
of the lost energy, and arrived at the conclusion that the most economical
diameter can be computed within an accuracy of about 10% from
D0.52H^ 0.17(P/H)0.43 (12.27)
wherePis the rated capacity of the plant (kW), His the rated head (m),
andDis the diameter (m).
The design of the anchorages and support rings for the penstocks
(additional momentum forces) has to be carefully considered wherever
there is a change of gradient and direction at branch outlets. The treat-
ment of the subject is beyond the scope of this text; further information
can be found in structural design books. Surge tanks are dealt with in
Section 12.10.
520 HYDROELECTRIC POWER DEVELOPMENT
Fig. 12.18 Economic diameter of penstock
