Mass Conservation: 1‐D Open Channel Flow Equations

DeLong, Lewis L.

doi:10.1061/(asce)0733-9429(1989)115:2(263)

Cited by 10 publications

(6 citation statements)

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“…where q(s)ds is the differential for the total flow, dQ. Equation 52 also is the same result as developed by DeLong (1989).…”

Section: 3 Correction Coefficients For Channel Curvilinearitymentioning

confidence: 85%

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Full equations utilities (FEQUTL) model for the approximation of hydraulic characteristics of open channels and control structures during unsteady flow

Franz¹,

Melching²

1997

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The Full EQuations UTiLities (FEQUTL) model is a computer program for computation of tables that list the hydraulic characteristics of open channels and control structures as a function of upstream and downstream depths; these tables facilitate the simulation of unsteady flow in a stream system with the Full Equations (FEQ) model. Simulation of unsteady flow requires many iterations for each time period computed. Thus, computation of hydraulic characteristics during the simulations is impractical, and preparation of function tables and application of table look-up procedures facilitates simulation of unsteady flow. Three general types of function tables are computed: one-dimensional tables that relate hydraulic characteristics to upstream flow depth, two-dimensional tables that relate flow through control structures to upstream and downstream flow depth, and three-dimensional tables that relate flow through gated structures to upstream and downstream flow depth and gate setting. For open-channel reaches, six types of one-dimensional function tables contain different combinations of the top width of flow, area, first moment of area with respect to the water surface, conveyance, flux coefficients, and correction coefficients for channel curvilinearity. For hydraulic control structures, one type of one-dimensional function table contains relations between flow and upstream depth, and two types of two-dimensional function tables contain relations among flow and upstream and downstream flow depths. For hydraulic control structures with gates, a three-dimensional function table lists the system of two-dimensional tables that contain the relations among flow and upstream and downstream flow depths that correspond to different gate openings. Hydraulic control structures for which function tables containing flow relations are prepared in FEQUTL include expansions, contractions, bridges, culverts, embankments, weirs, closed conduits (circular, rectangular, and pipe-arch shapes), dam failures, floodways, and underflow gates (sluice and tainter gates). The theory for computation of the hydraulic characteristics is presented for open channels and for each hydraulic control structure. For the hydraulic control structures, the theory is developed from the results of experimental tests of flow through the structure for different upstream and downstream flow depths. These tests were done to describe flow hydraulics for a single, steady-flow design condition and, thus, do not provide complete information on flow transitions (for example, between free-and submerged-weir flow) that may result in simulation of unsteady flow. Therefore, new procedures are developed to approximate the hydraulics of flow transitions for culverts, embankments, weirs, and underflow gates. Abstract 1 1.2.1 Look-up Tables for Channel Cross Sections Cross sections of a stream usually are given in a series of horizontal distances from reference points, called offsets, and the elevation of points on the bed of the stream. The area of flow, the top width of the...

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“…where q(s)ds is the differential for the total flow, dQ. Equation 52 also is the same result as developed by DeLong (1989).…”

Section: 3 Correction Coefficients For Channel Curvilinearitymentioning

confidence: 85%

“…Therefore, equation 49 can be expressed as 50where integration is over area and the arguments for all the functions are dropped. Equation 50 is the same result as developed by DeLong (1989). These same operations applied to equation 46 result in…”

Section: 3 Correction Coefficients For Channel Curvilinearitymentioning

confidence: 99%

Full equations utilities (FEQUTL) model for the approximation of hydraulic characteristics of open channels and control structures during unsteady flow

Franz¹,

Melching²

1997

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“…The weight coefficients for computing volumes and momentum content have been developed previously. Weight coefficients have been developed for equations similar to equations 41 and 44 by DeLong (1989) and Froehlich (1991). DeLong presented a momentum equation that did not include a weight coefficient on any term except the momentum-content term.…”

Section: Integral Form For Curvilinear Alignmentmentioning

confidence: 99%

“…Froehlich questioned this result and derived a correction factor for the friction term given by k(s) ds, (45) where s is the offset distance across the cross section as measured from a reference point on the channel bank, h(s) is local depth in a cross section at cross-section offset s, qw(s) is the flow per unit width in a cross section at offset s, k(s) is the conveyance per unit width in a cross section at offset s, G(s) is the rate of change of distance along the flow line at offset s to the rate of change of distance along the channel axis (sinuosity at offset s), and SB and SE are the offset at the beginning and end of the wetted top width for the cross section. DeLong (1991) pointed out that the total conveyance applied by Froehlich (1991) was not adjusted for sinuosity and was computed assuming that the friction slope was the same for each flow line across the section. If the total conveyance is adjusted for sinuosity and the local conveyance adjusted for sinuosity is substituted into equation 45, then Mf = 1 and, therefore, does not appear in the equations.…”

Section: Integral Form For Curvilinear Alignmentmentioning

confidence: 99%

Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

Franz¹,

Melching²

1997

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“…and Equations 1 through 4 are similar to those presented by Cunge and others (1980) with two exceptions: they have been extended to include the volumetric effects of sinuosity with the inclusion of metric coefficients, M a and M q (DeLong 1986), and density is assumed uniform in cross section but not necessarily constant with stream distance or time. The area-weighted sinuosity coefficient, M a (DeLong 1989), may vary both with depth of flow and distance and is defined by…”

Section: Governing Equationsmentioning

confidence: 99%

The computer program FourPt (Version 95.01), a model for simulating one-dimensional, unsteady, open-channel flow

1997

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FourPt is a computer program capable of computing unsteady one-dimensional flow in networks of open-channels. Optionally, governing equations may represent dynamic-wave, diffusion-wave, or kinematic-wave equations and may include variable channel sinuosity and variable water density. If density is allowed to vary, density values must be supplied by the user as this version of FourPt does not currently compute transport or heat flow. Governing equations are converted to a set of linearized equations using a four-point-implicit finite-difference method with Newton-Raphson iteration. The resulting set of simultaneous equations are solved directly by Gaussian elimination. Optional boundary conditions include known flow, water-surface elevation, water-surface slope, and three-parameter ratings. Additionally, a facility exists for users to program their own boundary constraints. Logarithmic and semi-logarithmic stage-discharge relations and dam-break functions also may be used as boundary constraints and are included in the program code as examples of user-programmed boundary constraints. Channel cross sections may be represented by rectangular, trapezoidal, or irregular geometry, depending on which geometry routines are linked with the program code. Spacing of user-supplied channel cross sections is independent of the selection of spatial discretization for numerical solution. FourPt is written in FORTRAN 77 using a data-encapsulation programming paradigm. This report describes data input and output and demonstrates selected model capabilities with examples.

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Mass Conservation: 1‐D Open Channel Flow Equations

Cited by 10 publications

References 0 publications

Full equations utilities (FEQUTL) model for the approximation of hydraulic characteristics of open channels and control structures during unsteady flow

Full equations utilities (FEQUTL) model for the approximation of hydraulic characteristics of open channels and control structures during unsteady flow

Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

The computer program FourPt (Version 95.01), a model for simulating one-dimensional, unsteady, open-channel flow

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