Standard step method: Difference between revisions

Revision as of 17:46, 3 December 2013

Revision as of 17:57, 3 December 2013

Line 47:

[[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) ===

Line 61:

</big>

'''Step 1:''' Determine if the reach is steep or mild

[[File:Step 1.jpg|Step 1]]

'''Step 2:''' Determine the effect of the Sluice Gate on flow

[[File:Step 2.jpg|Step 2]]

'''Step 3:''' Develop a sketch of the surface water profile

[[File:Step 3 (STM method).jpg|Step 3 (STM method)]]

Using Figure 3 and knowledge of the upstream and downstream conditions and the depth values on either side of the gate, a general estimate of the profiles upstream and downstream of the gate can be generated. Upstream, the water surface must rise from a normal depth of 0.97 m to 9.21 m at the gate. The only way to do this on a mild reach is to follow an M1 profile. The same logic applies downstream to determine that the water surface follows an M3 profile from the gate until the depth reaches the conjugate depth of the normal depth at which point a hydraulic jump forms to raise the water surface to the normal depth.

'''Step 4:''' Use the Newton Raphsom Method to solve the M1, M2, and M3 surface water profiles. The solution presented explains how to solve the problem in a spreadsheet, explaining how to calculate values column by column. Note, only calculations for the M1 profile will be shown below.

'''Step 4:''' Use the Newton Raphson Method to solve the M1 and M3 surface water profiles. The upstream and downstream portions must be modeled separately with an initial depth of 9.21 m for the upstream portion, and 0.15 m for the downstream portion. The downstream depth should only be modeled until it reaches the conjugate depth of the normal depth, at which point a hydraulic jump will form. The solution presented explains how to solve the problem in a spreadsheet, showing the calculations column by column. Within Excel, the goal seek function can be used to set column 15 to 0 by changing the depth estimate in column 2 instead of iterating manually.

[[File:STM Method (Step 4).jpg|STM Method (Step 4)]]<br />

Line 81:

[[File:Surface Water Profiles (Calculated).jpg|Surface Water Profiles (Calculated)]]

Normal depth was achieved at approximately 2,200 meters upstream of the gate.

'''Step 6:''' Solve the problem in the HEC-RAS Modeling Environment:

It is beyond the scope of this Wikipedia Page to explain the intricacies of operating HEC-RAS. For those interested in learning more, the HEC-RAS user’s manual is an excellent learning tool and the program is free to the public. It is also important to note, the example problem is a simplified situation, where minor energy losses due to expansion/contraction and the sluice gate are not taken into account. To adequately model this within the HEC-RAS modeling environment, a sluice gate constant (Cs¬) was determined and minor loss coefficients were set to zero.

The first two figures below are the upstream and downstream water surface profiles modeled by HEC-RAS. There is also a table provided comparing the differences between the profiles estimated by the two different methods at different stations to show consistency between the two methods. While the two different methods modeled similar water surface shapes, the standard step method predicted that the flow would take a greater distance to reach normal depth upstream and downstream of the gate. This stretching is caused by the errors associated with assuming average gradients between two stations of interest during our calculations. Smaller dx values would reduce this error and produce more accurate surface profiles.

:<math>Q = C_s*b*y_g*(2*g*H_{T,1})^{1/2}</math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <big>'''Sluice Gate Equation'''</big>

There are four figures below illustrating the “steady flow” HEC-RAS results. The first figure is a graphical output directly from HEC-RAS, showing the surface water profile of the modeled reach. The next three figures are comparing the surface water profiles developed by HEC-RAS and the STM calculation method. There is good agreement between HEC-RAS and the STM method, except for the M3 profile just downstream of the sluice gate. While HEC-RAS can model both subcritical and supercritical flows within the same reach, but in this instance, it did not produce an M3 Profile.

[[File:HEC-RAS Output 2.jpg|HEC-RAS Output 2]]

The HEC-RAS model calculated that the water backs up to a height of 9.21 meters at the upstream side of the sluice gate, which is the same as the manually calculated value. Normal depth was achieved at approximately 1,700 meters upstream of the gate.

HEC-RAS modeled the hydraulic jump to occur 18 meters downstream of the sluice gate.

[[File:Tabularcomparison.jpg|Tabularcomparison]]

== References ==