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5.3 Capacity and Size of Conduits 173
change to elastic energy. Then the spring would vibrate back and forth. In a pipe, compres-
sion of the water and distention of the pipe wall replace the compression of the spring. The
behavior of the pressure wave and the motion of the spring and the water are identically de-
scribed by the differential equations for one-dimensional waves. Both systems would vi-
brate indefinitely, were it not for the dissipation of energy by internal friction.
Water hammer is held within bounds in small pipelines by operating them at moder-
ate velocities, because the pressure rise in psi or kPa cannot exceed about 50 times the
velocity expressed in ft/s or m/s. In larger lines the pressure is held down by arresting
flows at a sufficiently slow rate to allow the relief wave to return to the point of control
before pressures become excessive. If this is not practicable, pressure-relief or surge
valves are introduced.
Very large lines, 6 ft (1.8 m) or more in equivalent diameter, operate economically
at relatively high velocities. However, the cost of making them strong enough to with-
stand water hammer would ordinarily be prohibitive if the energy could not be dissi-
pated slowly in surge tanks. In its simplest form, a surge tank is a standpipe at the end
of the line next to the point of velocity control. If this control is a gate, the tank accepts
water and builds up back pressure when velocities are regulated downward. When
demand on the line increases, the surge tank supplies immediately needed water and
generates the excess hydraulic gradient for accelerating the flow through the conduit.
Following a change in the discharge rate, the water level in a surge tank oscillates
slowly up and down until excess energy is dissipated by hydraulic friction in the
system.

5.3 CAPACITY AND SIZE OF CONDUITS

With rates of water consumption and fire demand known, the capacity of individual supply
conduits depends on their position in the waterworks system and the choice of the designer
for (a) a structure of full size or (b) duplicate lines staggered in time of construction.
Minimum workable size is one controlling factor in the design of tunnels.
Otherwise, size is determined by hydraulic and economic considerations. For a gravity
system, that is, where pumping is not required, controlling hydraulic factors are avail-
able heads and allowable velocities. Head requirements include proper allowances for
drawdown of reservoirs and maintenance of pressure in the various parts of the commu-
nity, under conditions of normal as well as peak demand. Reservoir heads greater than
necessary to transport water at normal velocities may be turned into power when it is
economical to do so.
Allowable velocities are governed by the characteristics of the water carried and the
magnitude of the hydraulic transients. For silt-bearing waters, there are both lower and
upper limits of velocity; for clear water, only an upper limit. The minimum velocity
should prevent deposition of silt; it lies in the vicinity of 2 to 2.5 ft/s (0.60 to 0.75 m/s).
The maximum velocity should not cause erosion or scour, nor should it endanger the con-
duit by excessive water hammer when gates are closed quickly. Velocities of 4 to 6 ft/s
(1.2 to 1.8 m/s) are common, but the upper limit lies between 10 and 20 ft/s (3 and 6.1 m/s)
for most materials of which supply conduits are built and for most types of water carried.
Unlined canals impose greater restrictions. The size of force mains and of gravity mains
that include power generation is fixed by the relative cost or value of the conduit and the
cost of pumping or power.
When aqueducts include more than one kind of conduit, the most economical distribu-
tion of the available head among the component classes is effected when the change in cost