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360. Online publications featuring online calculations [230630] |  |
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360. Online publications featuring online calculations [230630] | |
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ABSTRACT. A review of rating curve concepts is accomplished. The curve depicts the relationship between discharge and stage at a given point in a stream or river. Under steady uniform flow, the rating is unique, i.e., there is one value of discharge for each value of stage. However, the situation is complicated under unsteady flow conditions. Depending on the flow, the rating may actually be nonunique, typically showing a histeresis, i.e., a nonsingular value of discharge as a function of stage, and vice versa. Further complications arise if the flow is actually able to move its bed, as it is typically the case in alluvial channels in the absence of geologic controls. In medium-sized to large rivers, the flow acts to minimize the changes in stage, effectively reducing the variability in stage between low flows and high flows. Nature accomplishes this feat by increasing form friction during low flows, by way of bedforms, such as ripples and dunes, and by obliterating the bedforms during high flows. This effectively reduces form friction to negligible amounts, leaving grain friction as the only acting type of friction. Lastly, unsteady sediment transport may also cause alterations in rating curves. Some very active rivers may be aggrading; yet, others may be degrading. Active rivers may substantially change their cross section and/or course/alignment during major floods. Invariably, shifts in rating are the net result of these geomorphic processes. |
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ABSTRACT:
A study of the effect of cross-sectional shape on free-surface channel
hydrodynamic
instability is accomplished. At the outset, the rating exponent β, Froude number
F, and Vedernikov number V are identified
as the controlling variables.
A steep, lined channel is specified for the analysis.
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| ABSTRACT: The theoretical basis for Clark's original 1945 and Clark's Ponce 1989 methods of catchment routing are explained and compared. It is shown that Ponce's method consistently provides a somewhat longer time base and a correspondingly smaller peak discharge than Clark's original methodology. This is a direct consequence of Ponce's use of a continuous time-area derived unit hydrograph, in lieu of the discrete hyetograph used by Clark. However, the differences in peak discharge are consistent with the methodologies used and do not appear to be significant. |
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| ABSTRACT: The Lane et al. (1959) theory for the equilibrium shape of self-formed channels in noncohesive alluvium has been revisited, with all assumptions and derivations clearly stated. The results are used to estimate self-formed top-width/maximum-depth ratios as a function of: (1) the friction angle of the noncohesive material forming the bed, and (2) the lift-to-drag force ratio acting on the particles. The findings may be used as a point-of-start in the study of unsteady alluvial channel morphology. |
| ABSTRACT: The differential equation for the dissolved oxygen sag curve (DO sag curve) is derived. The solution of this differential equation can be shown to be essentially the same as that of the well known Streeter-Phelps equation (Streeter and Phelps, 1925). Unlike the latter, the differential equation derived herein can be solved numerically and, therefore, does not require integration. Moreover, the differential equation is valid for all deoxygenation and oxygenation constants, unlike the Streeter-Phelps equation, which is undefined when these constants are equal. Two online calculators: (a) single case, and (b) general case, round up the analysis. |
| ABSTRACT: A verification of the Muskingum-Cunge flood routing method is accomplished by comparing theoretically calculated peak outflow and travel time with those generated using the constant-parameter Muskingum-Cunge method. The remarkably close agreement between analytical and numerical results underscores the utility of Muskingum-Cunge routing as a viable and accurate method for practical applications in flood hydrology. |
| ABSTRACT:
The source of a large river system, for example, the Missouri river, is often taken
as the location of the uppermost spring in the farthest tributary.
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| ABSTRACT:
The design of a lined channel, with a steep slope, to be hydraulically
stable is governed by the well-known Vedernikov criterion. However,
it can be shown that this depends on the shape of the cross section,
whether trapezoidal, rectangular, or triangular. For a given section,
there is a unique relationship between the exponent β of the
rating curve Q - A (discharge vs flow area), and the value
of V /F,
in which V = Vedernikov number, and F =
Froude number. In this work we use the onlinechannel15b
calculator to calculate the value of β and the corresponding
Vedernikov number for a rectangular, trapezoidal, or triangular
cross section. Three series of tests are carried out in a hypothetical
channel, keeping constant
discharge Q, Manning's n,
and bottom slope S, and varying the value of
the side slope z: (a) 0.25; (b) 0.5, and (c) 1. It is
concluded that when the bottom width b is reduced, the
Vedernikov number V is reduced more quickly
to values less than 1 for the lower values of z in the range |
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ABSTRACT:
The theoretical foundations and relevant experience with open-channel flow instability are
examined with the objective of controlling roll waves.
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| ABSTRACT: A comparison between the conventional approach to the hydrologic balance and L'vovich's catchment wetting approach, referred herein as the cybernetic approach, reveals fundamental conceptual differences. The conventional approach is seen to be mostly suited to event hydrology, particularly for applications of flood hydrology and related urban hydrology. On the other hand, the cybernetic approach is suited to yield hydrology, i.e., for determinations of the availability of water resources on an annual basis. |
| ABSTRACT: An online calculator has been developed and tested using the Muskingum-Cunge method to solve the classical Thomas problem of flood routing. The calculator can vary peak inflow, time base, and channel length. The choice for peak inflow qp (cfs/ft) is: (a) 200, (b) 500, and (c) 1,000. The choice for time base Tb (hr) is: (a) 48, (b) 96, and (c) 192. The choice for channel length L (mi) is: (a) 200, and (b) 500. The results are in agreement with analytical results of the Thomas problem. |
| ABSTRACT: The inherently stable channel is reviewed, elucidated, and calculated online. Theoretically, such a channel will become neutrally stable when the Froude number reaches infinity. Thus, constructing an inherently stable channel provides an unrealistically high factor of safety against roll waves. This suggests the possibility of designing instead a conditionally stable cross-sectional shape, for a suitably high but realistic Froude number such as F = 25, for which the risk of roll waves would be so small as to be of no practical concern. |
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| ABSTRACT: Henderson's formulations of the energy-based and momentum-based limiting contraction ratios are reviewed (Henderson 1966). Henderson's explicit energy-based equation is found to be correct, however, his implicit momentum-based equation is found to be incorrect. A new explicit momentum-based equation is derived, rendering the implicit formulation unnecessary. An online calculator enables the calculation of the limiting contraction ratio for both energy and momentum formulations. |
ABSTRACT:
The Penman-Monteith combination method for the
calculation of evaporation is reviewed and clarified. Unlike the original Penman
model, in the Penman-Monteith model the mass-transfer evaporation rate
is calculated based on physical principles. An illustrative example is worked out to show the
computational procedure. An online calculation using
ONLINE PENMAN-MONTEITH gives the same
answer.
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| ABSTRACT: This document provides a tabular comparison of several sharp-crested weirs for discharge measurement in open-channel flow. The following weirs are considered: (1) V-notch, fully contracted; (2) V-notch, partially contracted; (3) Cipolletti; (4) rectangular; (5) standard contracted rectangular; and (6) standard suppressed rectangular. Descriptions follow the USBR Water Measurement Manual. |
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| ABSTRACT: An online calculator of the Shuttleworth-Wallace method for calculating evapotranspiration from sparse crops is developed. The method can be used to complement evapotranspiration calculations based on the Penman-Monteith method. |
| ABSTRACT: Gradually varied flow water-surface profiles are expressed in terms of the critical slope Sc. In this way, the flow-depth gradient dy/dx is shown to be strictly limited to values outside the range encompassed by Sc and So, in which So is the bed slope. This new approach improves and completes the definition of flow-depth-gradient ranges in the analysis of water-surface profiles. Online calculators are provided to round up the experience. |
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