Mechanics of Fluids

oughness coefficient n is independent of the depth of flow. In fact, n may
increase by as much as 25% as the depth is reduced from d to about d/4,
so depths for maximum discharge and maximum mean velocity are slightly
underestimated by the simple analysis. Although it might seem desirable to
design such a conduit to operate under the conditions giving maximum discharge,
the corresponding value of h/d is so near unity that in practice the
slightest obstruction or increase in frictional resistance beyond the design
figure would cause the conduit to flow completely full.
The circular shape is frequently modified in practice. For example, when
large fluctuations in discharge are encountered oval or egg-shaped sections
(Fig. 10.11) are commonly used. Thus at low discharges a velocity high
enough to prevent the deposition of sediment is maintained. On the other
hand, too large a velocity at full discharge is undesirable as this could lead
to excessive scouring of the lining material.
10.8 SIMPLE WAVES AND SURGES IN OPEN CHANNELS
The flow in open channels may be modified by waves and surges of various
kinds which produce unsteady conditions. Any temporary disturbance of
the free surface produces waves: for example, a stone dropped into a pond
causes a series of small surface waves to travel radially outwards from the
point of the disturbance. If the flow along a channel is increased or decreased
by the removal or insertion of an obstruction – for example, by the sudden
opening or closing of a sluice gate – surge waves are formed and propagated
Simple waves and surges in open channels 427
Fig. 10.9
Fig. 10.10
Fig. 10.11