ABSTRACT
In the more general case, applicable to non-rectangular channels of slope angle 0:
22.1.1.1 The Bernoulli theorem and critical flow
Two important concepts in the hydraulics of flow through structures are the Bernoulli and pressure-momentum theorems. The former (see page 5/8) expresses conservation of energy, and when applied to straight-line flow in an open channel, taking bed level as reference level, may be expressed as:
H = d+ at V2/2g (22. l)
where H is the specific energy head, d the depth of flow above the bed, at coefficient, V the mean velocity and g the gravitational constant
Where the flow is curvilinear, depth will vary across the channel and d is a mean value. Under normal conditions of flow in wide uniform channels, at---1.02 for smooth boundaries but higher for rough boundaries. For example, if n/a~/6=O.0225 (where n--Manning's roughness factor) at = 1.12. In order to simplify calculations where velocity head is relatively small, at is often assumed to be unity. Head loss must be allowed for in the value of H. For channels of rectangular cross-section, Equation (22. I) can also be expressed as:
H= d+ atq2/2gd 2 (22.2)
where q is the discharge per unit width of channel Q/B where Q is the total discharge and B the width
To derive d from known H and q, with at= 1 Figure 22.1 may be used.
