Standard step method: Difference between revisions

Revision as of 14:03, 17 November 2013

Revision as of 17:46, 3 December 2013

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:<math>F_n=\frac{v}{(g\frac{A}{B})^{0.5}}</math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <big>'''Equation 2'''</big>

Under steady state flow conditions (e.g. no flood wave), open channel flow can be subdivided into three types of flow: uniform flow, gradually varying flow, and rapidly varying flow. Uniform flow describes a situation where flow depth does not change with distance along the channel. This can only occur in a smooth channel that does not experience any changes in flow, channel geometry, roughness or channel slope. During uniform flow, the flow depth is known as normal depth (yn). This depth is analogous to the terminal velocity of an object in free fall, where gravity and frictional forces are in balance (Moglen, 2013).<ref>{{cite web|last=Moglen|first=G.|title=Lecture Notes from CEE 4324/5894: Open Channel Flow, Virginia Tech|url=http://filebox.vt.edu/users/moglen/ocf/index.html|accessdate=April 24, 2013}}</ref> Typically, this depth is calculated using the [[Manning formula]]. Gradually varied flow occurs when the change in flow depth per change in flow distance is very small. In this case, hydrostatic relationships developed for uniform flow still apply. Examples of this include the backwater behind an in-stream structure (e.g. dam, sluice gate, weir, etc.), when there is a constriction in the channel, and when there is a minor change in channel slope. Rapidly varied flow occurs when the change in flow depth per change in flow distance is significant. In this case, hydrostatics relationships are not appropriate for analytical solutions, and continuity of momentum must be employed. Examples of this include large changes in slope like a spillway, abrupt constriction/expansion of flow, or a hydraulic jump.

== Water Surface Profiles (Gradually Varied Flow) ==

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:* The slope is relatively small

:* The Channel cross-section is prismaticknown at <math>(\frac{da}{dy}stations =of 0)</math>interest

:* There is a hydrostatic pressure distribution

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[[File:NewtonRaphsonMethod.jpg|NewtonRaphsonMethod]]

*Computer programs like excel contain iteration or goal seek functions that can automatically calculate the actual depth instead of manual iteration.

=== Conceptual Surface Water Profiles (Sluice Gate) ===