Chezy Coefficient Research Articles

Extrapolation of rating curves

A linear relation was established between vav and hav for open channel flows, which is confirmed by the hydrometric data for a large number of rivers and gauging sites. This relation is a more accurate characteristic of the river flow than that obtained by the Chezy formula, which requires, moreover, the determination of additional parameters.

Stability of Turbulent Roll-Waves in an Inclined Open Channel

This paper considers the roll-wave phenomenon out shallow turbulent flow down an inclined open channel. On the assumptions of long wave lengths and the Chezy formula for bottom resistance, Dressler has obtained periodic permanent roll-wave solutions with discontinuous water jumps. There exists a one-parameter family of possible wave trains for prescribed average discharge rate. However, if unstable wave trains are contained, they will not be realized. The linear stability of the permanent roll-wave train is then investigated to examine what wave trains are unstable in the family. They are shown to be unstable if their wave lengths are shorter than a certain critical value.

Palaeohydraulics of a tabular, cross-stratified sand in the Brampton Esker, Ontario

Several hydraulic techniques were used to estimate the flow depth (0.3 m) associated with the deposition of a tabular set (micro-delta) of cross-stratified sand in the Brampton esker. The competency of the flow, deduced from both the grain size and structural characteristics of the set, gave a value of approximately 0.65 m/sec for the palaeo-velocity of the flow. Estimates of palaeo-depth and velocity facilitated calculation of the Froude and Reynolds numbers, about 0.38 and 1.24 · 10 5, respectively. Extrapolation of other parameters included bed shear stress τ 0 (4.50 N/m 2), shear velocity U * (0.067 m/sec), dimensionless Chezy coefficient C/√ g (9.7), slope of the energy gradient S(0.00153), Darcy-Weisbach friction factor f(0.085), Manning roughness coefficient n(0.027) and discharge of bed-material load (19 metric tons/day/m). The figures cited are reasonable estimates only. The occurrence of regressive ripples in the bottomset of the micro-delta aided in the hydraulic interpretation. These flow characteristics are only representative of the final stages of deposition at one location on the flank of the esker. The core of the esker was probably deposited under different hydraulic conditions.

Surface Roughness Effects on Overland Flow

ABSTRACT SEVEN surfaces of widely differing surface configura-tion were examined with respect to their physical sur-face roughness and hydraulic characteristics. The sur-face roughness was characterized using spectral analysis, amplitude-separation techniques and area-wetted perimeter methods. The hydraulic behavior of the sur-faces was tested using flow equations incorporating ex-pressions of the roughness of the surfaces. Of the single parameter flow equations tested, both the Manning and Chezy equations were superior. Multiple parameter equations obtained higher correlations, but were con-sidered to be of less practical value.

Studies on finite amplitude waves in bounded water bodies

The problem treated here is the dynamics of a bay where water is driven through its opening periodically in time. The basic equations are expressed in the two horizontal coordinates and time and they are obtained by an integration of the Navier-Stokes equations in the vertical coordinate. The equations are nonlinear because of the convective terms in the acceleration. The problem of harbor dynamics provides a natural parameter as the ratio of mass of water entering the bay through the waves to the total mass of water in the bay. This small parameter multiplies the nonlinear terms and thus the problem is ideally suited for a perturbation analysis. The nonlinear terms are responsible for the generation of secondary flows and are particularly important near resonant frequences. The analysis further indicates the existence of a time independent flow analogous to acoustic streaming, known from solutions of the Navier-Stokes equations. The question of vorticity is studied and is seen that: a constant dissipation coefficient precludes the generation of vorticity even for the nonlinear case: and that only a weak (second order) vorticity can exist in the case of a variable dissipation term expressed through the Chezy coefficient. The study suggests also a semi analytic-numerical scheme with savings of 0(10 2) for irregular geometries through the separation of the various order harmonics as opposed to the usual integration in time.

The tides of the East River, New York

The East River, New York, is a cooscillating tidal strait connecting New York Harbor to western Long Island Sound. Linear wave theory is applied to the river in an attempt to interpret the tidal characteristics. The theory accurately describes the observed longitudinal variation in amplitude of the tidal current, but the simple model used does not adequately predict the amplitudes of the tidal heights or the overtides. The frictional resistance to flow through the river is characterized by an effective value of De Chezy's coefficient of ∼26 m½ s−1. Tidal current records gathered over a 5-day period from a linear array placed across the Upper East River have been analyzed to investigate the harmonic content of the tidal transport. The semidiurnal frequency and its third harmonic (M6) are dominant.

Roughness Coefficients Of Vegetated Flood Plains

The results of a model investigation to determine the roughness coefficients of vegetated flood plains are presented in this Report. Two types of vegetation are dealt with: hedges and orchards. The Chezy coefficient of the flood plain is mainly influenced by the average spacing between the hedgerows, the number of trees per unit area, and the water depth over the flood plains. Some applications are shown of the relationships derived from the calculations of river stages during very high discharges of the River Maas.

Relation of the parameters of velocity profiles to hydraulic resistances

A general izat ion and analysis of the results of investigations conducted to cheek the known formulas and to refine the boundary values of k on the basis of hydrologic data for mountain r iven with small values of the Chezy coefficient and for piedmont and lowland rivers with large values of this coefficient confirmed the appl icabi l i ty of G. V. Zheleznyakov's formulas [2, 5] and the validi ty of the upper l imi t of the parameter k= kma x-

Comparison of various formulas for determining the Chezy coefficient

1. Equation (1) is presently the best substantiated by full-scale observations for R≤3 m. 2. The complexity of Eq. (2) for determining the variable exponent y necessitates resorting to specially calculated tables of CηR or to simpler equations. 3. For the range 0.3<R<5 m we can recommend also Eq. (5) which gives for this range deviations not exceeding ±(1–2)% of C by Eq. (1). 4. For 5<R<10 m we can recommend for determining C Eq. (6) or simpler Eq. (4), the results of calculating C by which coincide with Eq. (6). 5. Equation (1) with values of the exponent y determined from Eqs. (10) and (11) can also be used for calculating C. 6. The collection of full-scale data on the value of C for rivers and canals with values hav>5 m is quite useful and expedient for a more complete substantiation of Eqs. (10) and (11) [4, 6].

Mount Etna and the 1971 eruption - Rheological features of the 1971 Mount Etna lavas

Rheological studies on the 1971 M ount Etna lavas indicate they underwent rapid transition from Newtonian to non-Newtonian fluids near their point of emission and that the non-Newtonian regime may be coincidental with high mechanical energy/low heat energy regime further from the boccas. Darcy’s equation quantifies the surface roughness of channels using the Chezy coefficient and is plotted against Reynolds number on a Stanton diagram. The relation is linear, and the critical value Re0 is not exceeded, proving wholly laminar flow. The lava underwent a divergent, twin spiral motion involving two dimensional laminar flow. Convergent, twin spiral motion occurred only where lava passed through a constriction at a relatively high velocity.

Comparison of formulas without roughness coefficients for determining the average stream velocity in rivers

As long ago as in the 19th Century various investigators proposed several empir ica l formulas for determining the average stream veloci ty in rivers which did not include roughness coeflicient~ (the formulas of Hessle, Hermanek. Greger, Matakevich, e t al . , [1, 2]). The exclusion of these coefficients is possible owing to the circumstance that in a natural flow roughness is closely related with the character of the flow: its discharge rate, slope, width, depth, etc, The empir ica l formulas for the Chezy coefficient which do not include the roughness coefficient have a complete ly different structure, which hampers their comparison with each other. However, i f we use the morphomet~ic relations which include the main geometric and hydraulic elements of the flow, such a comparison is possible. Of the large number of such relations proposed, we used the formulas of N. V. Lapturev [3] based on treatment of ex tensive data of ful l-scale observations on lowland rivers: h=0.52Q~ s~*, B = 4,66Q ~ = 12.5h t ,5 i=0.00028Q-O,= =0.00057h-O.,.

Determination of the time of travel along the river network

Hydrological forecasts are needed for successful flood control. The present article is concerned with the problem of the determination of the time of travel along the river network. On the basis of Chezy's formula a new approach to the problem is proposed. It includes a new empirical coefficient k used to characterize the ratio between the hydraulic radii of two river cross-sections, which define a given river reach. The value of k becomes stable when the discharge increases. This stabilization causes a preservation of the isochrone system for fairly high values of the discharge. The final formula is used in the solution of several examples, including plotting the isochrone system. Then a model of a flood wave hodograph may be drawn.Some properties of the time of travel and its distribution, along the river network are discussed. The influence of the lateral inflow may be expressed by a family of curves.

Geometric and Frictional Effects on Sudden Releases

The effects of resistance and channel cross-sectional geometry on the waves of sudden release are investigated. The analytical treatment follows Dressler's approach with the modification that channel cross-sectional geometry is included. Results obtained by the analysis include water surface profiles, mean velocity distribution and trajectory of positive wave front for different Chezy coefficients in rectangular, parabolic and triangular cross-sections.

Computation of Chezy's coefficient for streams

Computation of Chezy's coefficient for streams

Nonlinear Gravity Waves in a Thin Sheet of Viscous Fluid

In the study of long gravity waves of finite amplitude, the main body of the existing theories has been built upon the simplifying assumption that the viscosity is either totally negligible, or adequately described by an empirical law. To date very little systematic account of the viscosity effect has appeared that is based on the Navier-Stokes' equations of motion. Thus, in the important problems of flood waves in rivers, Chezy's formula and a variety of empirical laws of hydraulics have been used to replace the viscous stress terms, and this is the approach taken in most of the hydraulic studies on open channel flows. Among theoretical contributions along this line, one may mention the book by Stoker (1957), the works of Dressler (1949), and of Lighthill and Whitham (1955, I). Dressler developed a rigorous theory of roll waves. In particular he obtained a discontinuous periodic solution in the case of relatively large amplitudes and a continuous periodic (cnoidal) solution in the case of small amplitudes. General flood movement in long rivers has been masterfully investigated by Lighthill and Whitham (1955, I), as a type of kinematic waves. Their method of predicting the transient motion of large amplitude waves with discontinuities (or shocks) is especially noteworthy.

UNIFORM FLOW OF WATER IN ALLUVIAL CHANNELS.

The flow of water in canals and rivers in alluvial beds is analysed, and it is shown that the uniform flow of water in alluvial channels is of two types: (1) where bed material is not inm ovement and (2) where bedm aterial is in movement. It is shown that for (1) friction varies directly as velocity and Chezy's formula can be written as V=cRS. For (2) friction varies as the square of velocity and Chezy's formula retains its old form V= Cd/RSc; and C are constants for the particular type of bed material and are dependent on the coefficient of friction found by Froude from his experiments. The formulae V= cRS and V= Cd/RS are shown to be dimensionally correct. A formula for silt transportation iasr rived at tof ind out what maximum silt charge can be carried at a velocity. This formula is also shown to be dimensionally correct. The Froude coefficient of friction is correlated with diameter of bed material so that the values of c and C can be obtained from the average weighted mean diameter of bed material in millimeters. It is also suggested that a channel is stable when the velocity required to overcome friction equals the velocity required to transport suspended silt. The word silt used in the paper refers to inorganic matter carried by water either as bed load or in suspension.

A Discharge Diagram For Uniform Flow in Open Channels

This paper introduces a diagram of discharge stage and slope or fall relation for uniform flow in open channels. It is based on the Chezy formula wherein, for a constant stage, the discharge varies as the square root of the slope or fall and is designed to give the discharges at any stage for the falls that create the resulting discharges.