Abstract
Steady open channel flow is generally non-uniform. In gradually-varied flows, the changes of depth and velocity in space are small, so that streamline curvature effects can be neglected. If the channel bottom slope is small, then the hydrostatic vertical pressure distribution prevails.
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Notes
- 1.
In the present context, a steep slope implies that the normal depth is below the critical depth. However, a steep slope as used here shall be “mild” physically, that is, 1 + S2o ≈ 1. Otherwise slope corrections are necessary in the GVF Eq. (3.3) [see Chap. 1, Eq. (1.151)]. A steep slope in hydraulic structures implies that 1 + S2o > 1, to be discussed at the end of this chapter.
- 2.
The reader is warned that Bresse’s solution appeared mistyped in many publications in the form \( \Phi (u) = \frac{1}{6}\ln \left[ {\frac{{u^{2} + u + 1}}{{(u - 1)^{2} }}} \right] - \frac{1}{{3^{1/2} }}\tan^{ - 1} \left( {\frac{{3^{1/2} }}{2u + 1}} \right) + C_{1} \), which is obviously not the solution. Jan (2014, p. 24) detailed the integration process step-by-step. The typo appears to originate from C. J. Posey in Rouse (1950, p. 613).
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Castro-Orgaz, O., Hager, W.H. (2019). Computation of Steady Gradually-Varied Flows. In: Shallow Water Hydraulics. Springer, Cham. https://doi.org/10.1007/978-3-030-13073-2_3
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