Closure to “Multiple Critical Depth Occurrence in Two-Stage Cross Sections: Effect of Side Slope Change” by Ali R. Vatankhah

2014 ◽  
Vol 19 (9) ◽  
pp. 07014002
Author(s):  
Ali R. Vatankhah
Keyword(s):  
Cross Sections ◽  
Critical Depth ◽  
Two Stage ◽  
Side Slope ◽  
Slope Change

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.

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

Bending of Beams with Nonlinear Material Characteristics

1980 ◽  
Vol 102 (4) ◽  
pp. 776-780 ◽  
Author(s):  
G. Szuladzinski
Keyword(s):  
Cross Sections ◽  
Elevated Temperatures ◽  
Strain Curve ◽  
Bending Moment ◽  
Nonlinear Material ◽  
Stress Strain ◽  
Slope Change ◽  
Deflection Analysis ◽  
Manual Methods ◽  
Bending Of Beams

When an expression is known for the curvature of a beam as a function of a bending moment, it is a simple matter to determine the deflected shape. It is a bigger problem to obtain such an explicit expression using a realistic stress-strain curve. This paper begins with a Ramberg-Osgood type of stress-strain formula, that is characterized by a continuous slope change typical of metals in elevated temperatures. A moment-curvature equation of a similar form is then developed and its accuracy is verified for several basic cross-sections. The advantage of this approach is to improve the accuracy and efficiency of deflection analysis compared with the existing manual methods.

scholarly journals Two-stage description of charge distributions in 56Fe+p spallation reactions at 0.3-1.5 GeV/A

2021 ◽  
Vol 252 ◽  
pp. 07001
Author(s):  
N.G. Nicolis ◽  
G.A. Souliotis ◽  
A. Bonasera
Keyword(s):  
Gamma Rays ◽  
Cross Sections ◽  
Good Description ◽  
Stage Model ◽  
Reaction Products ◽  
Preliminary Calculation ◽  
Two Stage ◽  
Fragment Separator ◽  
Charge Distributions ◽  
Spallation Reactions

Spallation reactions are studied in the framework of a two-stage model. The intra-nuclear cascade (INC) stage of the reaction is simulated with the code ISABEL and a Constrained Molecular Dynamics (CoMD) code. The de-excitation of the highly excited pre-fragments is described with the multi-sequential binary decay code MECO, based on a generalized Weisskopf-Ewing formalism. Emission of nucleons, gamma rays and IMFs in their ground, excited bound and unbound states is considered. Calculated cross sections are compared with the experimental charge distributions of 56Fe + p spallation reaction products studied at GSI with the fragment separator FRS in the energy-range 0.3 − 1.5 GeV/A. At all bombarding energies, a good description of the experimental data is obtained with ISABEL-MECO using a global set of parameters. A preliminary calculation with CoMD-MECO at 1GeV/A is discussed.

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

Second Paper: An Investigation into the Effects of Pre-Heat Temperature on Ductility in a Warm Heading Process

1969 ◽  
Vol 184 (1) ◽  
pp. 885-895 ◽  
Author(s):  
P. F. Thomason
Keyword(s):  
Mild Steel ◽  
Surface Quality ◽  
Transfer Process ◽  
Surface Defects ◽  
Critical Depth ◽  
High Ductility ◽  
Two Stage ◽  
Heat Temperature ◽  
Solid Film ◽  
Artificial Surface

Two-stage warm heading operations were carried out on a mild steel and three high tensile bolt materials (types 1, 2 and 4 from B.S. 3111:1959) at pre-heat temperatures in the range from ambient up to 600°C. The tests were carried out in the form of a transfer process (approximately 2 seconds delay between stages) and also as an interrupted process (approximately 30 minutes delay between stages). Artificial surface defects of various depths were machined on the heading specimens to aid measurements of the change in ductility with increase in pre-heat temperature. The method consisted of estimating the critical depth of groove which would be just on the point of fracture at the end of a particular heading operation. The steels tested were found to have low ductility at pre-heat temperatures in the range from 200°C to 300°C; at a pre-heat temperature of 600°C the steels exhibited extremely high ductility. The results suggest that rolled bar of relatively poor surface quality could be warm headed at 600°C without fracturing. A solid film of colloidal graphite and a high chlorine oil were both found to be satisfactory lubricants at all specimen pre-heat temperatures up to 600°C.

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