chapter 3 hydraulics of open channel flow
chapter 3 hydraulics of open channel flow
chapter 3 hydraulics of open channel flow
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3.14 Chapter Three<br />
HYDRAULICS OF OPEN CHANNEL FLOW<br />
TABLE 3.4 Equivalent Roughness Values <strong>of</strong> Various Bed Materials<br />
Material k k<br />
(ft) (m)<br />
(1) (2) (3)<br />
Brass, copper, lead, glass 0.0001–0.0030 0.00003048–0.0009<br />
Wrought iron, steel 0.0002–0.0080 0.0001–0.0024<br />
Asphalted cast iron 0.0004–0.0070 0.0001–0.0021<br />
Galvanized iron 0.0005–0.0150 0.0002–0.0046<br />
Cast iron 0.0008–0.0180 0.0002–0.0055<br />
Wood stave 0.0006–0.0030 0.0002–0.0009<br />
Cement 0.0013–0.0040 0.0004–0.0012<br />
Concrete 0.0015–0.0100 0.0005–0.0030<br />
Untreated gunite 0.01–0.033 0.0030–0.0101<br />
Drain tile 0.0020–0.0100 0.0006–0.0030<br />
Riveted steel 0.0030–0.0300 0.0009–0.0091<br />
Rubble masonry 0.02 0.0061<br />
Straight, uniform earth 0.01 0.0030<br />
<strong>channel</strong>s<br />
Natural streambed 0.1000-3.0000 0.0305-0.9144<br />
Sources: From Ackers C (1958), Chow (1959), and Zegzhda (1938).<br />
With regard to Eq. (3.41), it is pertinent to observe that as R increases (equivalent to<br />
an increase in the depth <strong>of</strong> <strong>flow</strong>), n increases. Approximate values <strong>of</strong> k for selected<br />
materials are summarized in Table 3.4. For sand-bed <strong>channel</strong>s, the following sediment<br />
sizes have been suggested by various investigators for estimating the value <strong>of</strong> k: k � d 65<br />
(Einstein, 1950), k � d 90 (Meyer-Peter and Muller, 1948), and k � d 85 (Simons and<br />
Richardson, 1966).<br />
3.4.4 Resistance in Compound Channels<br />
In many designed <strong>channel</strong>s and most natural <strong>channel</strong>s, roughness varies along the perimeter<br />
<strong>of</strong> the <strong>channel</strong>, and it is necessary to estimate an equivalent value <strong>of</strong> n for the entire<br />
perimeter. In such cases, the <strong>channel</strong> is divided into N parts, each with an associated wetted<br />
perimeter (P i ), hydraulic radius (R i ), and roughness coefficient (n i ), and the equivalent<br />
roughness coefficient (n e ) is estimated by one <strong>of</strong> the following methods. Note that the wetted<br />
perimeter does not include the imaginary boundaries between the subsections.<br />
1. Horton (1933) and Einstein and Banks (1950) developed methods <strong>of</strong> estimating n e<br />
assuming that the average velocity in each <strong>of</strong> the subdivisions is the same as the<br />
average velocity <strong>of</strong> the total section. Then<br />
��<br />
N<br />
� i � 1<br />
ne �� P<br />
�P 3/2<br />
ini �<br />
�2/3<br />
(3.42)<br />
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