# Showing papers in "Journal of Hydraulic Engineering in 1972"

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TL;DR: In this paper, a linear relationship between the logarithm of the total sediment concentration and the effective unit stream power was shown to dominate the sediment concentration in an alluvial channel, where the coefficients in the proposed equation were related to particle size and water depth.

Abstract: A thorough study of the existing applicable data reveals the basic reason that previous equations often provide misleading predictions of the sediment transport rates. The error stems from the unrealistic assumptions made in their derivations. Unit stream power, defined as the time rate of potential energy expenditure per unit weight of water in an alluvial channel, is shown to dominate the total sediment concentration. Statistical analyses of 1,225 sets of laboratory flume data and 50 sets of field data indicate the existence and the generality of the linear relationship between the logarithm of total sediment concentration and the logarithm of the effective unit stream power. The coefficients in the proposed equation are shown to be related to particle size and water depth, or particle size and width-depth ratio. An equation generalized from Gilbert's data can be applied to natural streams for the prediction of total sediment discharge with good accuracy.

319 citations

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TL;DR: A method of analyzing flow distribution in hydraulic networks is presented which uses a linearized head loss term which allows a network of n pipes to be described by a set of n linear equations which can be solved simultaneously for the flow distribution.

Abstract: A method of analyzing flow distribution in hydraulic networks is presented. Basically, this method uses a linearized head loss term which allows a network of n pipes to be described by a set of n linear equations which can be solved simultaneously for the flow distribution. Because of the linear approximations used, several trials will be required to get an accurate solution. This method of analyzing hydraulic networks is characterized by an assured convergence which is very rapid when compared to other available methods. One reason for this is that it is possible to compute a fairly accurate initial flow distribution and no initial estimates are required. In addition, the method applies directly to both closed loop systems and open-closed loop systems. The method is also easy to program for solution on a digital computer.

239 citations

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TL;DR: In this article, an experimental investigation of the flow over sharp edged side-weirs in rectangular channels is reported, covering subcritical and supercritical flow regimes with weirs of zero as well as finite height.

Abstract: An experimental investigation of the flow over sharp edged side-weirs in rectangular channels is reported. The experiments cover subcritical and supercritical flow regimes with weirs of zero as well as finite height. The subcritical flow experimental data agree well with the derived analytical expression for the variation of the De Marchi coefficient with the Froude number of the main channel flow. The De Marchi coefficient for the side weirs of finite height has been found to be essentially the same as for the corresponding side-weir of zero height.

212 citations

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TL;DR: In this paper, the authors used step-wise multiple regression to develop equations for predicting delivery ratios and showed that the most important watershed characteristic, slope of the main stem channel, explains about 99% of the variation in delivery ratios.

Abstract: Sediment yield from watersheds is predicted by modifying the Universal Soil Loss Equation and using a delivery ratio. All factors of the equation except the rainfall factor are modified to increase computational efficiency. In addition, the erosion-control-practice factor is expanded to include the separate effect of grassed waterways. Delivery ratios are computed for five small blackland watersheds and related to watershed characteristics. Step-wise multiple regression was used to develop equations for predicting delivery ratios. The regression analysis showed that the most important watershed characteristic, slope of the main stem channel, explains about 99% of the variation in delivery ratios. The modified Universal Soil Loss Equation and the equation for predicting delivery ratios form a sediment yield model that should be useful in reservoir design and water quality studies.

206 citations

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TL;DR: In this article, it is shown that a simple kinematic model for erosion of sand beds in a long contraction, first proposed by Straub, can be modified for application to erosion around spur dikes.

Abstract: The present status of research on erosion of sand beds around spur dikes is briefly reviewed. The experimental results of erosion of two different sizes of nearly uniform sand are presented. It is shown that a rather simple kinematic model for erosion of sand beds in a long contraction, first proposed by Straub, can be modified for application to erosion around spur dikes. The equilibrium depth of scour depends on the size of the sand and the flow depth upstream of the location of the spur dike. This is consistent with Laursen's observations around bridge piers.

185 citations

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TL;DR: In this article, the surge wave in the tunnel is described after Meyer-Peter and Favre, and an experimental study is presented which describes the phenomena and gives verification to the numerical mode.

Abstract: Transients may arise in a hydraulic system such that flow conditions may alternate between free surface and submerged or pressurized behavior. Analytical considerations begin with the open-channel surge equations, and the resulting method-of-characteristics solution. The surge wave in the tunnel is described after Meyer-Peter and Favre. At the free-surface, pressurized interface, a method of solution similar to the movement of a hydraulic bore is arrived at. An experimental study is presented which describes the phenomena and gives verification to the numerical mode. As an application the Wettingen system is analyzed and shown to agree favorably with earlier results.

94 citations

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TL;DR: In this paper, a graph-theoretic model was developed for the analysis of nonlinear pipe networks, where the nonlinearities associated with components in the network are treated as an integral part of the formulation procedures and thus they do not require any special treatment.

Abstract: Graph-theoretic models were developed for the analysis of nonlinear pipe networks. Both symbolic formulation procedures as well as illustrative examples were presented. The topological information contained in the continuity equations together with the component characteristics are used to derive the minimum set of independent equations in a systematic manner. In contrast to conventional methods, the nonlinearities associated with components in the network are treated as an integral part of the formulation procedures and thus they do not require any special treatment. One of the main advantages of the graph-theoretic approach is that the formulation procedure is independent of the numerical technique used to solve the resulting set of nonlinear equations. In other words, once the equations are formulated, a suitable numerical method for solution can be chosen. The graph-theoretic formulation procedures are highly computer worthy.

89 citations

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78 citations

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TL;DR: In this paper, the authors show that a dimensionless bed-load discharge q *b = q b /U *b D g can be expressed as a function of a boundary Reynolds number, where q b is defined as the discharge volume per unit width and time.

Abstract: Experimental data show that a dimensionless bed-load discharge q *b = q b /U *b D g can be expressed as a function of a boundary Reynolds number R *b = U *b D g /ν and a dimensionless shear stress τ *b = τ ob /(γ s -γ)D g in which q b = bedload discharge in volume per unit-width and time; U *b = (τ ob /ρ) 1/2 = shear velocity; τ ob = bed shear stress; ρ = density of the water; D g = geometric mean size of sediment, ν = kinematic viscosity in the water, and γ and γ s are, respectively, the specific weight of water and sediment Contours of Q *b plotted on a Shields graph (ie, τ* vs R *b ) have the same shape as the Shields curve and the contour, q *b = 10 -2 , follows it closely The effect of temperature on τ o and q sb is shown by the data For R *b o and τ *b and an increase in R *b , q sg and q *b For 20 *b ob , τ *b and R *b and a decrease in q sb and q *b > 200 there is no temperature effect

70 citations

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TL;DR: In this article, the hydraulic jump in a horizontal, smooth-walled channel of rectangular cross section is studied both analytically and experimentally, and it is shown that jumps with developed inflow are longer, lower and subject to higher and more uniformly distributed skin friction than jumps with undeveloped inflow.

Abstract: The particular aspect of the jump phenomenon considered in the paper concerns the condition of inflow, i.e., the state of flow development of the supercritical stream. Based on an unconventional concept of longitudinal extent, the hydraulic jump in a horizontal, smooth-walled channel of rectangular cross section is studied both analytically and experimentally. It is shown that jumps with developed inflow are longer, lower and subject to higher and more uniformly distributed skin friction than jumps with undeveloped inflow. The latter have shear distributions which reveal a tendency toward separation with increasing Froude number. The trend is verified by the observed behavior of jumps with undeveloped inflow at Froude number as large as 30. Semi-empirical, closed-form relationships between sequent depth ratio and Froude numbers are derived and checked against experimental evidence.

65 citations

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TL;DR: In this paper, a new method for flood-frequency analysis using the concept of mixed distributions is developed using a mixture of only two component distributions is shown to fit the various observed flood distributions.

Abstract: A new method for flood-frequency analysis is developed using the concept of mixed distributions. A mixture of only two component distributions is shown to fit the various observed flood distributions. The two-distribution method is tested using annual flood series from 33 streams in Illinois. The flood distributions computed by this method fit the observed flood distributions better than other methods in use, insofar as the mean of absolute deviations of the computed floods from those observed is the least. The proposed method satisfactorily matches the medium and high floods which are of great interest to the engineers and hydrologists. An objective methodology has been formulated for computer application. The methodology is free from errors and uncertainties that exist when third and higher order moments are used for obtaining estimates of the component distribution parameters.

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TL;DR: In this paper, an equation for predicting the average annual sediment yield from sheet erosion is developed through multiple regression analysis, where a climatic factor as an indirect expression of vegetative cover, the average watershed slope, and two soil factors are the variables used.

Abstract: An equation for predicting the average annual sediment yield from sheet erosion is developed through multiple regression analysis. Most of the variation in yield is explained with data obtained by measurement of four watershed characteristics. A climatic factor as an indirect expression of vegetative cover, the average watershed slope, and two soil factors are the variables used. A good correlation of computed with measured sediment yields is obtained except at the lower rates of sedimentation. Improvements in predictive value can be achieved with experience in judging the necessary adjustments in the vegetative cover factor, through more intensive soil sampling and by use of only longtime sediment yields as the dependent variable. The data selected for this analysis are intended to exclude the influence of extensive gully or stream bank erosion on sediment yield.

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TL;DR: In this paper, a mathematical model is developed to predict the occurrence and behavior of ice ripples that form on the underside of river ice-covers, where the local rate of freezing or melting at the ice-flow interface is related to the difference between the local heat transfer rates by conduction through the ice and by turbulent transfer from the flow to the ice.

Abstract: A mathematical model is developed to predict the occurrence and describe the properties and behavior of ice ripples that form on the underside of river ice-covers. The local rate of freezing or melting at the ice-flow interface is related to the difference between the local heat transfer rates by conduction through the ice and by turbulent transfer from the flow to the ice. The local heat flux to the interface from the flow is expressed as a small perturbation expansion in terms of the steepness of the monochromatic interfacial wave, and is assumed to be shifted relative to the interface wave. The analysis yields a stability criterion and expressions for the amplification rate and celerity of the ripples. Laboratory data are used to obtain values for the constants introduced into the theory and to corroborate the analytical results. Field data are examined in the light of the laboratory results.

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TL;DR: In this article, a differential equation is developed to describe the vertical temperature distribution in a stratified reservoir and solved numerically, and a comparison of predicted and measured temperatures from the laboratory and field indicates that the mathematical model is capable of reproducing measured temperature profiles to within an accuracy of approximately 1°C without requiring any parameters that must be determined from prior temperature measurements.

Abstract: A differential equation is developed to describe the vertical temperature distribution in a stratified reservoir and solved numerically. Outlet temperatures are an integration of temperatures from within the withdrawal layer, the thickness of which depends upon the degree of stratification. A comparison of predicted and measured temperatures from the laboratory and field indicates that the mathematical model is capable of reproducing measured temperature profiles to within an accuracy of approximately 1°C without requiring any parameters that must be determined from prior temperature measurements. A net vertical advection is the primary mechanism by which heat is transported from the surface to the reservoir outlet.

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TL;DR: In this paper, the NASH model was used to simulate the instantaneous UNIT HYDROGRAPHS on a WATERSHED for VARIOUS URBANIZATION FACTORS.

Abstract: AFTER A PRELIMINARY ANALYSIS OF SEVERAL CONCEPTUAL MODELS, THE SINGLE LINEAR RESERVOIR AND THE NASH MODEL WERE SELECTED FOR FURTHER STUDY. ANALYSIS OF ABOUT TWO HUNDRED STORMS FROM WATERSHEDS WITH DIFFERENT DEGREES OF DEVELOPMENT INDICATED THAT THE PARAMETERS OF THE AFOREMENTIONED TWO MODELS VARIED NOT ONLY WITH THE URBANIZATION FACTOR (RELATED TO THE RATION OF THE BUILT-UP AREA IN A WATERSHED TO THE TOTAL WATERSHED AREA) BUT ALSO WITH OTHER PHYSIOGRAPHIC AND METEOROLOGICAL FACTORS. REGRESSION RELATIONSHIPS BETWEEN THE PARAMETERS OF THE MODELS AND THE MORE SIGNIFICANT METEOROLOGICAL AND PHYSIOGRAPHIC FACTORS INCLUDING THE URBANIZATION FACTOR WERE DEVELOPED. THESE REGRESSION RELATIONSHIPS WERE USED TO SIMULATE THE INSTANTANEOUS UNIT HYDROGRAPHS ON A WATERSHED FOR VARIOUS URBANIZATION FACTORS. CHANGES IN RUNOFF FROM A WATERSHED WITH INCREASING URBANIZATION FACTORS WERE THEN SIMULATED FOR A VARIETY OF RAINFALL CHARACTERISTICS. /AUTHOR/

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TL;DR: In this paper, a nomograph based on the kinematic wave formulation is proposed as a design aid for determining the time of concentration for overland flow in flood hydrology.

Abstract: Recent studies indicate that the kinematic wave model provides a good approximation to the rising side of the overland flow hydrograph in most cases that are of interest in flood hydrology. A nomograph based on the kinematic wave formulation is proposed as a design aid for determining the time of concentration for overland flow. Results obtained with the kinematic wave model compare favorably with those obtained experimentally by the Corps of Engineers and Carl F. Izzard.

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TL;DR: In this article, the relationship between the concentration and the flow discharge per unit of channel width is defined and a graphical relationship between concentration and flow discharge is shown. But the relationship is not defined for coarse sand.

Abstract: Laboratory tests were conducted to define the relationships between the transport of fine sand and the flow variables. Data from 105 experiments with sand bed material having a median sieve diameter of 0.1 mm in a 100-ft (30.48 m)-long by 4-ft (1.22 m)-wide recirculating flume show that the concentration of the transported material depends in a rather complex, but consistent way on the basic flow variables. A graphical relationship between the concentration and the flow discharge per unit of channel width defines consistent curves of equal depth and readily delineates the various bed form regimes. A similitude analysis of published transport data for coarser sands suggests a single curve for concentration versus Froude number for each median sediment size. However, the data for the 0.1-mm material suggest separate curves of concentration versus Froude number for the different bed form regimes. The data for depths less than or equal to 0.7 ft (0.21 m) define a continuous relationship like that for coarser sands, but the data for deeper depths define an extended plane bed curve segment that has not been observed for coarser material.

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TL;DR: In this paper, a new integral method is devised to predict the behavior of buoyant jets discharged to infinite, flowing, stratified ambients through single submerged diffusers, based on an integration of the basic partial differential equations written in a natural coordinate system.

Abstract: A new integral method is devised to predict the hydrothermal behavior of buoyant jets discharged to infinite, flowing, stratified ambients through single submerged diffusers. The method, based on an integration of the basic partial differential equations written in a natural coordinate system, is more general than previous methods. In addition, a new generalized entrainment function is defined which includes the effects of internal turbulence, buoyancy, jet orientation, and cross flow. Only one of the four entrainment coefficients is obtained by fitting predictions to data. Theoretical predictions are compared with 29 different flows. Agreement between theory and data is good; this is particularly significant as the range in experimental flow variables is considerable and the four entrainment coefficients are maintained constant for all predictions.

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TL;DR: The modified Newton’s algorithm not only ensures convergence, but also reduces the number of iterations when compared with the classical Newton's algorithm.

Abstract: Because of the characteristics of the Jacobian matrix, modifications to the Newton’s approach of solving pipe networks can be done in such a way that convergence toward the solution is ensured, com...

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TL;DR: In this article, free-vortex velocity distribution and curvature are used to simulate the flow at the brink of smooth horizontal channels of various cross sections, including rectangular, triangular, and parabolic cross sections.

Abstract: When the flow from an open channel is discharged freely into the air, the depth at the brink can be often closely correlated with the flow rate. Free-vortex velocity distribution and curvature are used to simulate the flow at the brink of smooth horizontal channels of various cross sections. A summary of the analysis is given herein for exponential channels of rectangular, triangular, and parabolic cross sections. The final theoretical values are also given for trapezoidal and circular cross sections. The final relationships for the case of jetted shooting flow just upstream of the end section of a rectangular channel are also given.

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TL;DR: In this article, wind tunnel tests showed that the drag coefficient of angular shaped bodies is significantly affected by the intensity of the free stream turbulence, for some bodies an increase in intensity causes an increase of C D while for others a decrease in C D results.

Abstract: Contrary to popular opinion, wind tunnel tests showed that the drag coefficient of angular shaped bodies is significantly affected by the intensity of the free stream turbulence. For some bodies an increase in intensity causes an increase in C D while for others a decrease in C D results. Tests made on a vibrating body having a shape similar to an H beam showed that the amplitude of vibration was increased more than 200% with an increase in free stream turbulence. The change in coefficient of drag C D is attributed to two primary effects. The first is increased Reynolds stress in the region of the surface of separation which appears to cause an increase in C D and the other is reattachment of the flow to the body which may cause the C D to increase or decrease depending upon the shape of the body. The range of Reynolds numbers in these tests is limited to the relatively narrow span from approximately 5 x 103 to 7 x 104.

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TL;DR: In this article, the frontal thickness of an oil slick can be expressed as a function of a densimetric Froude number based on properties of the stream and the density of the oil.

Abstract: An oil slick contained on the surface of a flowing stream may be divided into two zones of influence; a frontal region where dynamic forces are dominant and a viscous zone where viscous stresses determine the form of the slick It is shown that the frontal thickness of an oil slick can be expressed as a function of a densimetric Froude number based on properties of the stream and the density of the oil Dynamic effects cause the interface to become unstable when the densimetric Froude number exceeds a critical value and retention of a slick under such conditions becomes impossible

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TL;DR: In this paper, the effects of free-stream turbulence on the drag coefficient of a circular cylinder were investigated experimentally in an air duct and the experiments were performed over a range of Reynolds number, based on mean velocity and cylinder diameter.

Abstract: The effects of free-stream turbulence on the drag coefficient of a circular cylinder were investigated experimentally in an air duct. The experiments were performed over a range of Reynolds number, based on mean velocity and cylinder diameter, from 1,350 < Re < 8,000. A constant temperature hot-film anemometer was used to determine the turbulence intensity which was between 1.2% < u′ < 21%. The range of the dimensionless turbulence scale was from 0.5 < ∂/D < 3.3, in which ∂ = the turbulence scale defined through the integral of auto-correlation function and D = the diameter of the cylinder. Two smooth circular cylinders were used. They were 1/4 in. and 1/2 in. 6.35 mm and 12.7 mm shell fraction. Quantitative results were obtained. Equations describing the relationship between the drag coefficient and turbulence characteristics were also obtained.

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TL;DR: In this paper, a theory is presented to predict the ultimate conditions of stable bed without a sensible change in slope, and the changes in bed roughness and in the regime of flow are both taken into consideration.

Abstract: The release of clear water from dams built across rivers running in alluvial sediments will cause bed degradation in the downstream channel. If this degradation went on unchecked, it would be a threat to the existing structures on the river, and might cause serious drainage problems in the cultivated areas on both sides of the river. A theory is presented to predict the ultimate conditions of bed armoring without sensible change in slope. The changes in bed roughness and in the regime of flow are both taken into consideration. The ultimate conditions of stable bed are obtained. The theory is then applied to the actual conditions of bed degradation of the Nile River after the closure of the Aswan High Dam in 1964. It is found that the general degradation in this particular case is not excessive, and does not need large scale protective measures or step-down weirs, to meet the probable change in the slope of river bed. However, the existing barrages on the Nile may need protection against any probable local or general scour.

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TL;DR: In this paper, the accuracy of all procedures used in evaluating flood frequency should be appraised in terms of standard error so that the proper flood risk can be obtained, and the true risk is evaluated by relating it to the standard error of estimate of the regression used to define the flood-frequency curve.

Abstract: Flood damage computed from flood-frequency curves fitted mathematically to observed annual peak flows or estimated by regression with basin characteristics, is a biased estimator of flood risk. The inaccuracy inherent in any flood-frequency curve increases the annual premium that would have to be charged to break even over a large number of projects. For ungaged sites where the population of annual peaks can be assumed to follow a log-Pearson Type III distribution, the true risk is evaluated by relating it to the standard error of estimate of the regression used to define the flood-frequency curve. In view of this relation between bias and error, the accuracy of all procedures used in evaluating flood frequency should be appraised in terms of standard error so that the proper flood risk can be obtained.

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TL;DR: In this article, it is shown that the position sensitivity of a hydraulic jump is dependent upon Froude number, boundary roughness and distance downstream from the gate, and that the jump is much more sensitive in a laminar boundary layer development region than in a fully developed turbulent flow.

Abstract: The rate of displacement of the toe of a hydraulic jump along a channel with respect to change in tailwater elevation is defined as the position sensitivity of the jump. The steady flow downstream of a model sluice gate is analyzed theoretically for the case of a laminar boundary layer developing from the vena contracta and breaking into fully developed turbulent flow. It is shown that the position sensitivity of the jump is dependent upon Froude number, boundary roughness and distance downstream from the gate. Experiments have been performed using a shallow stream of depth 0.26 in. (4.064 mm). The theoretical analysis is justified and the jump is shown to be much more sensitive in a laminar boundary layer development region than in a fully developed turbulent flow. In general, sensitivity is greater in laminar than turbulent flow, is decreased by an increase in boundary roughness and by an increase in Froude number. Because model tests are at a lower Reynolds number than corresponding full scale situations, model results for jump sensitivity are conservative.

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TL;DR: In this article, an equation to predict reaeration rates in natural streams and rivers with wind blowing along the water surface is theoretically developed and experimentally tested, and the experimental results give support to the theoretically developed equation.

Abstract: An equation to predict reaeration rates in natural streams and rivers with wind blowing along the water surface is theoretically developed and experimentally tested. The physical model used in the development of the equation consisted of interfacial layers of water that absorb gas at a rate proportional to an effective diffusion coefficient at the interface, and this surface water is then carried into the main body of liquid by the action of turbulence beneath the water surface. The experimental results give support to the theoretically developed equation. The results indicate that reaeration rates are significantly increased when waves appear on the surface. The increase is often much more than can be accounted for by the increase in surface area. The increase is attributed to the dynamic effect of waves and the wind-induced surface shear stress.

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TL;DR: In this paper, an analytical treatment for the problem of one-dimensional infiltration into a homogeneous porous medium is presented, where movement of both the air phase and the water phase and compressibility of the air are considered.

Abstract: An analytical treatment for the problem of one-dimensional infiltration into a homogeneous porous medium is presented. Movement of both the air phase and the water phase and compressibility of the air are considered. The procedure assumes that some capillary terms can be neglected in the saturation equation, whereas all capillary terms are retained in an integral equation for the unknown total flow. Infiltration rate curves are obtained for a number of situations involving different boundary or initial conditions or both. Comparisons are made with results of an earlier and simpler procedure, confirming the validity of the simpler procedure. It is recommended that the traditional unsaturated flow equation be abandoned in favor of the two-phase flow approach.

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TL;DR: In this paper, two formulas have been developed for the equivalent roughness coefficient in shallow open-channel flow for hydraulic computation in open channels and in channels with ice cover, respectively.

Abstract: Channel sections with different roughnesses along the water perimeter are often encountered in design problems. Typical design problems include partly lined canals and tunnels with different construction materials used at the bottom and the side. It is necessary to compute the equivalent roughness coefficient for any hydraulic computation in open channels and in channels with ice cover. Two formulas have been developed herein for the equivalent roughness coefficient in shallow open-channel flow.