scholarly journals Explicit equations for critical depth in open channels with complex compound cross sections. A discussion

2013 ◽  
Vol 29 ◽  
pp. 65-66 ◽  
Author(s):  
Hubert Chanson
Keyword(s):  
Cross Sections ◽  
Complex Compound ◽  
Open Channels ◽  
Critical Depth

scholarly journals On the Statistical Theory of Nuclear Reactions

1978 ◽  
Vol 31 (2) ◽  
pp. 151 ◽  
Author(s):  
WK Bertram
Keyword(s):  
Statistical Theory ◽  
Cross Sections ◽  
Nuclear Reactions ◽  
Reaction Cross ◽  
Open Channels ◽  
S Matrix ◽  
Reaction Cross Sections

The statistical theory of energy-averaged reaction cross sections is examined using the pole expansion of the S-matrix. Exact expressions for the average cross sections in terms of the parameters of the S-matrix are derived for the case when there are two open channels. It is shown that when the number of channels exceeds two, the average cross sections can be evaluated provided the poles of the S-matrix are evenly spaced.

Prediction of the lateral flow regime and critical depth in compound open channels

2009 ◽  
Vol 36 (1) ◽  
pp. 1-13 ◽  
Author(s):  
E. Kordi ◽  
S. A. Ayyoubzadeh ◽  
M. Z. Ahmadi ◽  
A. Zahiri
Keyword(s):  
Cross Sections ◽  
Specific Energy ◽  
Laboratory Data ◽  
Flow Distribution ◽  
Flow Regimes ◽  
Transitional Zone ◽  
Main Channel ◽  
Critical Depth ◽  
Single Cross Section ◽  
The Common

In this study, the common critical depth calculation in compound channels has been modified considering the effect of momentum transfer between the interface of a main channel and its floodplains. In noncorrected specific energy curves of a given slope, the flow is not necessarily entirely sub- or supercritical as it is in a single cross section and there is a possibility of both flow regimes at a certain stage, called the lateral mixed flow regimes, which makes the application of specific energy equation to determine the critical depth and transitional zone calculations questionable. In the present research, the flow distribution in a main channel and floodplains has been corrected by combining the corrected hydraulic flow in compound cross sections using the coherence method. The specific energy has been subsequently modified in the subsections. The results seem satisfactory when compared with the results based on the available laboratory data.

III. Hydraulic problems on the cross-sections of pipes and channels

1888 ◽  
Vol 44 (266-272) ◽  
pp. 101-109
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Open Channels ◽  
The Cross

In that division of hydromechanics which is devoted to the investigation of the flow of liquids through pipes and open channels, the resistance due to the friction of the contained liquid against the sides of the pipes or channels has led to expressions for the velocity as a function of the dimensions and shape of the cross-section commonly designated as the hydraulic mean depth. This quantity is defined as the quotient of the area of the cross-section of the liquid by that part of its perimeter in contact with the pipe or channel. In a full pipe this perimeter is identical with that of the pipe’s cross-section, and in practice this is generally a circle.

scholarly journals An approximate formula to calculate the critical depth in circular culvert

2020 ◽  
Vol 71 (7) ◽  
pp. 840-852
Author(s):  
Binh Hoang Nam
Keyword(s):  
Approximate Solution ◽  
Cross Sections ◽  
Approximate Solutions ◽  
Maximum Error ◽  
Regression Equations ◽  
Critical Depth ◽  
Design Engineers ◽  
Hydraulic Design ◽  
Long Time ◽  
True Values

Critical depth is a depth of flow where a specific energy section is at a minimum value with a flow rate. Critical depth is an essential parameter in computing gradually varied flow profiles in open channels and in designing culverts. If cross-sections are rectangular or triangular, the critical depth can be computed by the governing equation. However, for other geometries such as trapezoidal, circular, it is totally difficult to find a solution, because the governing equations are implicit. Therefore, the approximate solution could be determined by trial, numerical or graphical methods. These methods tend to take a long time to find an approximate solution, so a simple formula will be more convenient for consultant hydraulic design engineers. The existing formulas are simple, but the relative error between the approximate solutions and true values can reach 9% or greater. This article presents new explicit regression equations for the critical depth in a partially full circular culvert. The proposed formula is quite simple, and the relative maximum error is 3.03%. It would be very useful as a reference for design in conduit engineering

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