Smooth Rectangular Open Channels Research Articles

Semi-analytical method to estimate boundary shear stress in smooth rectangular and trapezoidal open channels

The boundary shear stress is obtained from the continuity and momentum equations in smooth prismatic open channels. Shear stress is a function of gravity, secondary flow, and gradient velocity. In this research, semi-analytical equations were obtained to estimate the average boundary shear stress in smooth rectangular and trapezoidal open channels by 0.5, 1, 1.5 and 2 side slopes using conformal mapping techniques. After dividing the channel cross section into the bed and wall sub-sections, the present study used the method by Guo and Julien (2005) to estimate the average shear stress of the bed and the wall in open channels. For the studied case, by the first shear stress estimation, secondary current and constant eddy viscosity were neglected. After recommending two secondary current and eddy viscosity correction factors, a second approximation well matched the experimental measurements of the average shear stress for all aspect ratios.

Bed and wall shear stresses in smooth rectangular channels

Various empirical equations for mean bed and wall shear stresses have been proposed for smooth rectangular open channels. Considering that the distribution of bed shear and wall shear stresses is affected by the cross-sectional shape, the gravity force based on the flow depth used to non-dimensionalize shear stresses in previous studies is modified to a parameter that includes the width and wetted-perimeter. This yields a new set of dimensionless equations for mean bed and wall shear stresses, and the wall/bed shear force ratio. These equations compared well with all available experimental data over a wide range of aspect ratios from 0.31 to 50. These equations also yield new relationships for bed and wall friction factors.

Entropy Wake Law for Streamwise Velocity Profiles in Smooth Rectangular Open Channels.

In narrow open channels, the three-dimensional nature of the flow and the transport momentum from the sidewalls to the central region cause the maximum longitudinal velocity to occur below the water surface. The entropy model is unable to accurately describe the velocities near the free surface when the dip phenomenon exists. The present paper proposes a new dip-modified entropy law for steady open channel flows, which consists of three additional terms: the first one similar to Coles’ function; the second one linearly proportional to the logarithmic distance from the free surface; and the third one depending on the cubic correction near the maximum velocity. The validity of the new model was tested on a set of laboratory measurements carried out in a straight rectangular flume with smooth boundaries and for different values of water discharge, bottom slope, and aspect ratio. A detailed error analysis showed good agreement with the data measured through the present research and a more accurate prediction of the velocity-dip-position compared with the one evaluated through the original entropy model. In addition, the modified entropy wake law matched very well with other literature data collected in rectangular cross-sections with different flow conditions.

Modified log-wake-law for smooth rectangular open channel flow

Smooth rectangular open channel flow is a benchmark for studying river hydraulics and sediment transport. Such a flow is more complicated than the classic boundary layer flow at least in two ways: (i) the maximum velocity occurs below the water surface, which is called the velocity-dip-phenomenon and (ii) the velocity distribution is affected not only by the channel bottom but also by the side-walls and the free surface. This fundamental flow is approximated herein by three hypotheses: (i) the velocity-dip-position shifts exponentially from the water surface to half flow depth as the width–depth ratio decreases from infinity to zero; (ii) the conventional wake-law for the centreline velocity distribution results from boundary shear stresses including the bottom, side-walls, and water surface in terms of secondary currents; and (iii) the cross-sectional velocity distribution is described by Guo and Julien's modified log-wake-law. These hypotheses are well supported by flume data.

Flow Resistance in Smooth Rectangular Open Channels with Low Aspect Ratios

This paper shows an approach that is useful for evaluating the resistance to flows in narrow open channels. A series of experiments were first carried out in a smooth, rectangular, open channel for which the aspect ratio varied from 0.12 to 1.53. Experimental data collected were then used to validate a resistance formula that was proposed previously by modifying Prandtl’s friction law.

Closure to “Evaluation of Flow Resistance in Smooth Rectangular Open Channels with Modified Prandtl Friction Law” by Nian-Sheng Cheng, Hoai Thanh Nguyen, Kuifeng Zhao, and Xiaonan Tang

Closure to “Evaluation of Flow Resistance in Smooth Rectangular Open Channels with Modified Prandtl Friction Law” by Nian-Sheng Cheng, Hoai Thanh Nguyen, Kuifeng Zhao, and Xiaonan Tang

Discussion of “Evaluation of Flow Resistance in Smooth Rectangular Open Channels with Modified Prandtl Friction Law” by Nian-Sheng Cheng, Hoai Thanh Nguyen, Kuifeng Zhao, and Xiaonan Tang

Discussion of “Evaluation of Flow Resistance in Smooth Rectangular Open Channels with Modified Prandtl Friction Law” by Nian-Sheng Cheng, Hoai Thanh Nguyen, Kuifeng Zhao, and Xiaonan Tang

Evaluation of Flow Resistance in Smooth Rectangular Open Channels with Modified Prandtl Friction Law

Flow resistance in open channels is usually estimated by applying the approach that is developed originally for pipe flows. Such estimates may be useful for engineering applications but always differ from measurements to some extent. This paper first summarizes empirical approaches that have been proposed in the literature to reconcile the resistance difference. These include various modifications of the pipe friction for applications to rectangular ducts and open channel flows. An improved friction equation is then derived for evaluating flow resistance of smooth rectangular open channels. Comparisons are made with experimental data reported by previous researchers and those collected in the present study. It is shown that the new proposed equation is applicable for both narrow and wide channels and is more accurate than those available in the literature.

Closure to “Shear Stress in Smooth Rectangular Open-Channel Flows” by Junke Guo and Pierre Y. Julien

Closure to “Shear Stress in Smooth Rectangular Open-Channel Flows” by Junke Guo and Pierre Y. Julien

Discussion of “Shear Stress in Smooth Rectangular Open-Channel Flows” by Junke Guo and Pierre Y. Julien

Discussion of “Shear Stress in Smooth Rectangular Open-Channel Flows” by Junke Guo and Pierre Y. Julien

Correlation and distribution of shear stress for turbulent flow in a smooth rectangular open channel

Calculation of shear stresses in open channel flow is very important in civil engineering applications such as structural design, determination of velocity distribution and sediment transport. It is argued in literature that the velocity distribution equations for pipe flow may be used in open-channel flow analysis. However, due to irregular boundary sheer stress, this claim seems to be unreasonable and the irregularities should be taken into consideration. In this study, wall shear stresses for turbulent flow in rectangular open channel are investigated. Using mean velocity measurements and assuming validity of the logarithmic velocity distribution perpendicular to wetted perimeter, dimensionless shear stresses in the unified velocity distribution are determined.A semi-theoretical method is applied for the solutions of non-linear equations.A shear stress distribution equation is proposed to calculate irregular boundary shear stresses on the wall and bed in smooth rectangular channels.

Shear Stress in Smooth Rectangular Open-Channel Flows

The average bed and sidewall shear stresses in smooth rectangular open-channel flows are determined after solving the continuity and momentum equations. The analysis shows that the shear stresses are function of three components: (1) gravitational; (2) secondary flows; and (3) interfacial shear stress. An analytical solution in terms of series expansion is obtained for the case of constant eddy viscosity without secondary currents. In comparison with laboratory measurements, it slightly overestimates the average bed shear stress measurements but underestimates the average sidewall shear stress by 17% when the width–depth ratio becomes large. A second approximation is formulated after introducing two empirical correction factors. The second approximation agrees very well ( R2 >0.99 and average relative error less than 6%) with experimental measurements over a wide range of width–depth ratios.

Discussion and Closure: Effect of Shape on Uniform Flow through Smooth Rectangular Open Channels

Discussion and Closure: Effect of Shape on Uniform Flow through Smooth Rectangular Open Channels

Discussion of “Effect of Shape on Uniform Flow through Smooth Rectangular Open Channels” by N. Narayana Pillai

Discussion of “Effect of Shape on Uniform Flow through Smooth Rectangular Open Channels” by N. Narayana Pillai

BOUNDARY SHEAR STRESS DISTRIBUTIONS IN SMOOTH RETANGULAR OPEN CHANNEL FLOWS.

Keywords NANYANG TECHNOLOGICAL UNIVERSITY, SINGAPORE SHEAR, STRESS, DISTRIBUTION, BOUNDARIES, SMOOTH, RECTANGULAR, OPEN, CHANNELS, FLOW, METHODS, ANALYTICAL, FLUIDS, THREE DIMENSIONAL, PERIMETER, WETTED, STEADY, UNIFORM, ASPECT, RATIOS, MODELS, MATHEMATICAL, HYDRAULICS, HYDRODYNAMICS, RIVERS, THEORY, MECHANISMS, ENERGY, TRANSPORTATION, INFLUENCE, ROUGHNESS, DISSIPATION... Show All

Mechanism of Energy Transportation and Turbulent Flow in a 3D Channel

This paper presents an analytical approach for the partitioning of the flow cross-sectional area in steady and uniform three-dimensional channels. The mechanism and direction of energy transport from the main flow are analyzed first. Based on the availability of surplus energy from the main flow, a concept of energy transportation through a minimum relative distance toward a unit area on the wetted perimeter is proposed. This leads to a novel method to analytically divide the flow area into various parts corresponding to the channel shape and roughness composition of its wetted perimeter. The demarcated boundary or “division line” can be evaluated using a presented equation. The existence of the division lines, which are lines of zero Reynolds shear stress within the flow region, has been proven through comparison with turbulence characteristics measurements. The method is illustrated in a study of the shear stress distribution in smooth rectangular open channels. Analytical solutions, valid for all aspect ratios, are derived for the mean side wall and bed shear stresses, and they compared well with existing experimental data from various researchers.

Effect of Shape on Uniform Flow through Smooth Rectangular Open Channels

Available experimental data on friction in smooth rectangular channels were analyzed by a re­ searcher and arrived at the relationship Ifyj = 2 log Ryf - 0.8, where R = 4VRlv and!, =1''JIp(PIR) for channels and!, =/for smooth pipes. 'JIp(PIR) is a shape parameter. Values of PIR when bly < 2 were indicated by an asterisk, and a relationship was obtained between PIR and 'JIp(PIR). Two researchers analyzed the same data that were used by another researcher and concluded that two functions 'JI,(Plb) = VPib and 'JI 2(bly) are required to reflect the shape parameter. However, they combined and obtained 'JI K = 'JI 'JI2 = IIJ'. 'JI 2(bly) was calculated and plotted against bly. They noted that 'JI K == I/'JIp, but maintained that there is no good relationship between 'JIp and PIR. In the present study, it is shown that based on the curve, the equation connecting 'JIp(PI R) and PIR could be obtained, which fits the curve within I% error. A plot PIR versus 'JIp(PIR) is given for ready use.

Flow Characteristics in a Gradually Expanded Rectangular Open Channel Flow

This study is concerned with flow chracteristics in a gradually expanding smooth rectangular open channel. The spatially evolution of mean velocity-, Reynolds stress-, and turbulent intensity-profiles in the longitudinal direction were investigated experimentally. Cole's wake parameter is expressed as a function of the pressure gradient, assuming the entire mean velocity profiles to be described by Cole's law. It is found that the distributions of Reynolds stress and turbulent intensities under the adverse pressure gradient differ substantially from these in the favorable pressure gradient.

Supercritical Flow in Smooth Open Channels

The effect of Reynolds number and Froude number on the friction factor is studied for supercritical turbulent flow in smooth rectangular open channels. The values of Froude numbers for various aspect ratios, beyond which the flow becomes unstable, are determined using the method of Berlamont and Vanderstappen and the measured momentum coefficients. For stable supercritical flows, the friction factor varies with Reynolds number only, as in the case of subcritical flows. For unstable supercritical flows, the friction factor is found to vary according to Rouse's equation.

The Von-Kármán coefficient in sediment laden flow

The paper presents the results of an experimental investigation on the behaviour of Von-Kármán coefficient in sediment laden flow in straight and in curved reaches of smooth rectangular rigid boundary open channels. The investigation shows the effect of varying the Reynolds number of sediment laden flow, the suspended sediment concentration in the flow, the radius-breadth ratio of the channel, and the central angle of the bend.