Standard step method: Difference between revisions

Revision as of 23:59, 24 April 2013

Revision as of 00:04, 25 April 2013

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==Standard Step Method Calculation==

The STM numerically solves equation 3 through an iterative process. This can be done using the bisection or Newton-Raphson Method, and is essentially solving for total head at a specified ___location using equations 4 and 5 by varying depth at the specified ___location. (<ref>{{cite book|last=Chaudhry|first=M.H.|title=Open-Channel Flow|year=2008)|publisher=Springer|___location=New York}}</ref>.<br /><br />

:<math>H_2 = H_1 - h_f</math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <big>'''Equation 4'''</big><br /><br />

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

[[File:Sluice Gate Sketch.jpg|thumb| '''Figure 4.''' Illustration of surface water profiles associated with a sluice gate in a mild reach (top) and a steep reach (bottom). ]]

Figure 4 illustrates the different surface water profiles associated with a sluice gate on a mild reach (top) and a steep reach (bottom). Note, the sluice gate induces a choke in the system, causing a “backwater” profile just upstream of the gate. In the mild reach, the [[hydraulic jump]] occurs downstream of the gate, but in the steep reach, the hydraulic jump occurs upstream of the gate. It is important to note that the gradually varied flow equations and associated numerical methods (including the standard step method) cannot accurately model the dynamics of a hydraulic jump (<ref>{{cite book|last=Chaudhry|first=M.H.|title=Open-Channel Flow|year=2008)|publisher=Springer|___location=New York}}</ref>. See the [[Hydraulic jumps in rectangular channels]] page for more information. Below, an example problem will use conceptual models to build a surface water profile using the STM.

==Example Problem==