Simplified Calculation Method of Normal Water Depth on II Type Horseshoe Tunnel with Flat-Bottom

2013 ◽  
Vol 353-356 ◽  
pp. 1353-1358
Author(s):  
Hui Wen ◽  
Feng Ling Li
Keyword(s):  
Cross Section ◽  
Water Depth ◽  
Maximum Error ◽  
Transcendental Equation ◽  
Structure Design ◽  
Flat Bottom ◽  
Relationship Analysis ◽  
Calculation Step ◽  
Normal Water ◽  
Simplified Calculation

Abstract: II type horseshoe with flat–bottom evolved from standard II type horseshoe cross-section. It is composed of a flat-bottom and three arc sections. It is commonly applied in the field of hydroelectric engineering. The normal water depth computation equation for II type horseshoe cross-section with flat–bottom tunnel is a transcendental equation and no analytic solution. In this paper, based on the mathematics transformation for the basis equation and the relationship analysis between the dimensionless normal water depth and the relative parameters, a simplified calculation formula is established for the calculation of normal water depth for II type horseshoe cross-section with flat–bottom tunnel according to the fitting principle. This method overcomes the shortage of other iterative trial calculating methods, such as complex calculation step, depend on the special chart and curve, and existed serious error. The formula is simply and the maximum error is less than 0.23% under the general engineering design range (ratio of normal water depth and arch radius is between 0.05 - 1.45). it can be used on the engineering designing practice and the edit of the handbook of hydraulic structure design.

The Direct Solution on Normal Water Depth of I Type Horseshoe Tunnel with Flat–Bottom

2012 ◽  
Vol 170-173 ◽  
pp. 1595-1600
Author(s):  
Hui Wen ◽  
Feng Ling Li
Keyword(s):  
Cross Section ◽  
Water Depth ◽  
Maximum Error ◽  
Transcendental Equation ◽  
Structure Design ◽  
Direct Solution ◽  
Flat Bottom ◽  
Relationship Analysis ◽  
Calculation Step ◽  
Normal Water

Abstract: I type horseshoe with flat–bottom evolved from standard I type horseshoe cross-section. It is composed of a flat-bottom and three arc sections. It is commonly applied in the field of hydroelectric engineering. The normal water depth computation equation for I type horseshoe cross-section with flat–bottom tunnel is a transcendental equation and no analytic solution. In this paper, based on the mathematics transformation for the basis equation and the relationship analysis between the dimensionless normal water depth and the relative parameters, a direct solution is established for the calculation of normal water depth for I type horseshoe cross-section with flat–bottom tunnel according to the fitting principle. This method overcomes the shortage of other iterative trial calculating methods, such as complex calculation step, depend on the special chart and curve, and existed serious error. The formula is simply and the maximum error is less than 0.3% under the general engineering design range (ratio of normal water depth and arch radius is between 0 to 1.4471). it can be used on the engineering designing practice and the edit of the handbook of hydraulic structure design.

A New Algorithm for Normal Water Depth of the Ordinary Arched Tunnel

2011 ◽  
Vol 250-253 ◽  
pp. 2902-2905
Author(s):  
Hui Wen ◽  
Feng Ling Li
Keyword(s):  
Water Depth ◽  
Maximum Error ◽  
Transcendental Equation ◽  
Structure Design ◽  
Linear Solution ◽  
Relationship Analysis ◽  
Calculation Step ◽  
Normal Water ◽  
New Formula ◽  
The Relationship

Arched section consisted of a rectangle and a semicircle part. It is commonly applied in the field of hydroelectric engineering. The normal water depth computation equation for an arched tunnel is a transcendental equation and no analytic solution. In this paper, based on the mathematics transformation for the basis equation and the relationship analysis between the dimensionless normal water depth and the relative parameters, a new linear solution formula are established for the calculation of normal water depth for arched section tunnel according to the fitting principle. This method overcomes the shortage of other iterative trial calculating methods, such as complex calculation step, depend on the special chart and curve, and existed serious error. The new formula is simply and the maximum error is less than 0.6156% under the general engineering design range (ratio of normal water depth and arch radius is between 1 to 1.5416). it can be used on the engineering designing practice and the edit of the handbook of hydraulic structure design.

Direct Calculation Formulae for Critical Depth of II Type Horseshoe Tunnel with Flat-Bottom

2013 ◽  
Vol 353-356 ◽  
pp. 1339-1344
Author(s):  
Feng Ling Li ◽  
Hui Wen
Keyword(s):  
Cross Section ◽  
Direct Calculation ◽  
Maximum Error ◽  
Transcendental Equation ◽  
Critical Depth ◽  
Flat Bottom ◽  
Relationship Analysis ◽  
Calculation Step ◽  
Complex Calculation ◽  
The Relationship

Abstract: II type horseshoe with flat–bottom evolved from standard II type horseshoe cross-section. It is composed of a flat-bottom and three arc sections. It is commonly applied in the field of hydroelectric engineering. The critical depth computation equation for II type horseshoe cross-section with flat–bottom tunnel is a transcendental equation and no analytic solution. In this paper, based on the mathematics transformation for the basis equation and the relationship analysis between the dimensionless critical depth and the relative parameters, a direct solution is established for the calculation of critical depth for II type horseshoe cross-section with flat–bottom tunnel according to the fitting principle. This method overcomes the shortage of other iterative trial calculating methods, such as complex calculation step, depend on the special chart and curve, and existed serious error. The formula is simply and the maximum error is less than 0.515% under the general engineering design range (ratio of critical depth and arch radius is located between the 0 - 1.60).

scholarly journals New and improved three and one-third parabolic channel and most efficient hydraulic section

2017 ◽  
Vol 44 (5) ◽  
pp. 387-391 ◽  
Author(s):  
Yan-Cheng Han ◽  
Said M. Easa
Keyword(s):  
Exact Solution ◽  
Cross Section ◽  
Water Depth ◽  
Open Channel ◽  
Hydraulic Characteristics ◽  
Explicit Formulas ◽  
Practical Applications ◽  
Normal Water ◽  
Wetted Perimeter ◽  
Approximate Formulas

Several parabolic-shaped open channel sections are available in the literature, including quadratic and semi-cubic parabolic sections. This paper presents a three and one-third parabolic cross-section that has superior characteristics compared to those of previous parabolic-shaped sections. The section characteristics, including two approximate formulas for the wetted perimeter and a simple iterative formula for the normal water depth are presented. The exact solution for the most efficient hydraulic section is derived. The results show the width–depth ratio for the most efficient hydraulic section is 2.1273. Practical applications of the proposed most efficient hydraulic section are presented, including direct formulas for the discharge and explicit formulas of normal and critical depths. The results show that the proposed section improves the hydraulic characteristics compared with other parabolic sections and trapezoidal section.

The propagation of gravity currents in a V-shaped triangular cross-section channel: experiments and theory

2014 ◽  
Vol 754 ◽  
pp. 232-249 ◽  
Author(s):  
Marius Ungarish ◽  
Catherine A. Mériaux ◽  
Cathy B. Kurz-Besson
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Viscosity Coefficient ◽  
Gravity Currents ◽  
Quantitative Agreement ◽  
Flat Bottom ◽  
Special Configuration ◽  
Theoretical Predictions ◽  
Speed Of Propagation ◽  
High Reynolds

AbstractWe investigate the motion of high-Reynolds-number gravity currents (GCs) in a horizontal channel of V-shaped cross-section combining lock-exchange experiments and a theoretical model. While all previously published experiments in V-shaped channels were performed with the special configuration of the full-depth lock, we present the first part-depth experiment results. A fixed volume of saline, that was initially of length $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}x_0$ and height $h_0$ in a lock and embedded in water of height $H_0$ in a long tank, was released from rest and the propagation was recorded over a distance of typically $ 30 x_0$. In all of the tested cases the current displays a slumping stage of constant speed $u_N$ over a significant distance $x_S$, followed by a self-similar stage up to the distance $x_V$, where transition to the viscous regime occurs. The new data and insights of this study elucidate the influence of the height ratio $H = H_0/h_0$ and of the initial Reynolds number ${\mathit{Re}}_0 = (g^{\prime }h_0)^{{{1/2}}} h_0/ \nu $, on the motion of the triangular GC; $g^{\prime }$ and $\nu $ are the reduced gravity and kinematic viscosity coefficient, respectively. We demonstrate that the speed of propagation $u_N$ scaled with $(g^{\prime } h_0)^{{{1/2}}}$ increases with $H$, while $x_S$ decreases with $H$, and $x_V \sim [{\mathit{Re}}_0(h_0/x_0)]^{{4/9}}$. The initial propagation in the triangle is 50 % more rapid than in a standard flat-bottom channel under similar conditions. Comparisons with theoretical predictions show good qualitative agreements and fair quantitative agreement; the major discrepancy is an overpredicted $u_N$, similar to that observed in the standard flat bottom case.

Hydrodynamic Properties of an Asymmetric Deepwater Riser Bundle

2006 ◽  
Author(s):  
Charles Zimmermann ◽  
Richard James ◽  
Blaise Seguin ◽  
Mattias Lynch
Keyword(s):  
Cross Section ◽  
Water Depth ◽  
Hydrodynamic Characteristics ◽  
Cfd Analysis ◽  
Effective Solution ◽  
Hydrodynamic Properties ◽  
Global System ◽  
Field Development ◽  
Hydrodynamic Behaviour ◽  
Deepwater Riser

The BP operated Greater Plutonio field development offshore Angola comprises a spread-moored FPSO in 1,300 m water depth, serving as a hub processing the fluids produced from or injected into the subsea wells. The selected riser system is a riser tower tensioned by a steel buoyancy tank at its top end and distributed foam buoyancy along a central structural tubular. The riser bundle is asymmetric in cross-section and this paper presents the work performed to determine the specific hydrodynamic characteristics of the design. Both basin tests and CFD analysis results are presented with discussion on some specific hydrodynamic issues: vortex-induced vibration (VIV) of the global riser tower system, VIV of individual risers, and the dynamic stability of the global system (i.e. galloping). Finally, guidelines for the assessment of the hydrodynamic behaviour of such system geometries are proposed. The results of this paper demonstrate that the Greater Plutonio riser bundle represents an effective solution in term of hydrodynamic behaviour and is not sensitive to VIV fatigue or galloping.

scholarly journals Slit-type Breakwater; Box-type Wave Absorber

1976 ◽  
Vol 1 (15) ◽  
pp. 154 ◽  
Author(s):  
Shoshichiro Nagai ◽  
Shohachi Kakuno
Keyword(s):  
Cross Section ◽  
Water Depth ◽  
Vertical Wall ◽  
Bottom Wall ◽  
Front Wall ◽  
Type Wave ◽  
Composite Type ◽  
New Type ◽  
Vertical Walls ◽  
Horizontal Bottom

A box-type wave absorber, which is composed of a perforated vertical front-wall and a perforated, horizontal bottom-wall, has been proved by a number of experiments to show lower coefficients of reflection and more distinguished reduction of wave pressures than the perforated vertical- wall breakwater. A breakwater of composite-type, which is 1500 m long and to be built at a water depth of 10 to 11 m below the Datum Line in the Port of Osaka, is being designed to set this new type of wave absorber in the concrete caissons of the vertical-walls which is named "a slit-type breakwater". The typical cross-section of the breakwater and the advantages of the slit-type breakwater are presented herein.

Structure design of caudal-fin-type piezoelectric-stack pump with variable cross-section oscillating vibrator

2011 ◽  
Vol 19 (6) ◽  
pp. 1334-1343 ◽  
Author(s):  
胡笑奇 HU Xiao-qi ◽  
张建辉 ZHANG Jian-hui ◽  
黄毅 HUANG Yi ◽  
夏齐霄 XIA Qi-xiao ◽  
黄卫清 HUANG Wei-qing
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Structure Design ◽  
Variable Cross ◽  
Caudal Fin

scholarly journals Scour around Spur Dike in Sand–Gravel Mixture Bed

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1417 ◽  
Author(s):  
Manish Pandey ◽  
Wei Haur Lam ◽  
Yonggang Cui ◽  
Mohammad Amir Khan ◽  
Umesh Kumar Singh ◽  
...  
Keyword(s):  
Water Depth ◽  
Velocity Ratio ◽  
Maximum Error ◽  
Length Ratio ◽  
Scour Depth ◽  
Spur Dike ◽  
Particle Ratio ◽  
Cause Of Failure ◽  
Equilibrium Scour Depth ◽  
Sediment Mixture

Scour is the main cause of failure for spur dike. The accurate prediction of scour around spur dike is essential to design a spur dike. The present study focuses on the maximum scour depth in equilibrium condition and parameters, which influence it in a sand–gravel mixture bed. Outcomes of the present experimental study showed that the non-dimensional maximum equilibrium scour depth increases with critical velocity ratio (U/Uca), water depth-armour particle ratio (h/da), Froude number for sediment mixture (Frsm), water depth-spur dike length ratio (h/l), and decreases with increase in armour particle-spur dike length ratio (da/l). The maximum scour depth is proportional to dimensionless parameters of U/Uca, h/da, Frsm, h/l, but the scour depth is inverse proportional to da/l. Scour around spur dike in a sand–gravel mixture is mainly influenced by the property of the sediment mixture. The scour increases with decrease in non-uniformity of the sediment mixture. A non-linear empirical equation is proposed to estimate the maximum scour depth at an upstream nose of rectangular spur dike with a maximum error of 15%. The sensitivity analysis indicates that the maximum non-dimensional equilibrium scour depth depends on Frsm, followed by the secondary sensible parameters da/l, h/l, and h/da.

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