360. Online publications featuring online calculations [230630] 

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 mediumsized 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. 

ABSTRACT: Two existing formulations for the coefficient of hydraulic diffusivity in diffusion wave modeling of catchment dynamics are evaluated. While the kinematic hydraulic diffusivity is independent of the Vedernikov number, the dynamic hydraulic diffusivity is dependent on the Vedernikov number. We use the script ONLINEOVERLAND, an analytical tool capable of considering either the kinematic or dynamic approaches to model hydraulic diffusivity. For this purpose, we use the reference test problem. Testing of the model varying the drainage area, plane slopes, rating exponent, and channel slope show the model's consistency in simulating catchment response under a variety of flow conditions. Calculated outflow hydrographs correctly show the type of catchment response, showing either superconcentrated, concentrated, or subconcentrated catchment flow, depending on the input data. The reference test problem is confirmed to depict a kinematic wave, effectively featuring zero wave diffusion. Therefore, the differences in outflow hydrograph between the two hydraulic diffusivities are shown to be negligible. For the general problem, which includes all types of shallowwater waves, i.e., kinematic, diffusion, and mixed kinematicdynamic, the use of the dynamic hydraulic diffusivity is recommended. 

ABSTRACT:
A study of the effect of crosssectional shape on freesurface 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.

 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 timearea 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. 

ABSTRACT:
The coefficients of the dimensionless partial differential equation of
convectiondiffusiondispersion of flood waves are derived, and shown to be
functions of the Froude and Vedernikov numbers only.

 ABSTRACT: The Lane et al. (1959) theory for the equilibrium shape of selfformed channels in noncohesive alluvium has been revisited, with all assumptions and derivations clearly stated. The results are used to estimate selfformed topwidth/maximumdepth ratios as a function of: (1) the friction angle of the noncohesive material forming the bed, and (2) the lifttodrag force ratio acting on the particles. The findings may be used as a pointofstart 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 StreeterPhelps 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 StreeterPhelps 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 MuskingumCunge flood routing method is accomplished by comparing theoretically calculated peak outflow and travel time with those generated using the constantparameter MuskingumCunge method. The remarkably close agreement between analytical and numerical results underscores the utility of MuskingumCunge 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.

 ABSTRACT:
The design of a lined channel, with a steep slope, to be hydraulically
stable is governed by the wellknown 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 

ABSTRACT:
The theoretical foundations and relevant experience with openchannel flow instability are
examined with the objective of controlling roll waves.

 ABSTRACT:
This article explores the properties of water, including physical, chemical, and biological properties. Most of the properties of water span more than one field, such as physics and chemistry, or chemistry and biology, or biology and physics. Understanding the nature of water requires a thorough interdisciplinary approach to science. 
 ABSTRACT: The classical Shields criterion for initiation of motion is expressed in terms of the Froude number and associated mean velocity required for initiation of motion in a sandbed channel. To solve the problem exactly, an iterative algorithm is developed to calculate these values using an online calculator. 
 ABSTRACT: The concepts of safe yield and sustainable yield of groundwater are analyzed and compared in the context of a hydrologic balance. It is surmised here that vertical recharge, i.e., the recharge originating in local precipitation, is the only recharge that may be tapped for capture by groundwater to avoid encroachment on established rights. A methodology to evaluate vertical recharge is developed and tested. The methodology is based on L'vovich's cybernetic hydrologic balance. This coefficient represents the fraction of precipitation that reaches the water table; therefore, it may be used to evaluate and assess sustainable groundwater yield. 
 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 MuskingumCunge 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 q_{p} (cfs/ft) is: (a) 200, (b) 500, and (c) 1,000. The choice for time base T_{b} (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 crosssectional 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. 
 ABSTRACT:
A comprehensive review of the amplitude and phase portraits of the MuskingumCunge method of flood routing is accomplished.
Expressions for the
amplitude and phase convergence ratios are developed as a function of:
(a) spatial resolution L/Δx; (b) Courant number C; and (c) weighting factor X.
It is concluded that the MuskingumCunge routing model is a good representation of the physical prototype, provided:
(1) the spatial resolution is sufficiently high,
(2) the Courant number is around 1, and
(3) the weighting factor is high enough in the range 
 ABSTRACT: The hydraulic design of a channel transition is described and explained. The calculation of an inlet transition between canal and flume is shown by an example, originally presented by Hinds (1928) and subsequently cited by Chow (1959). The example is reproduced with detailed explanation and minor corrections for rounding accuracy. An online calculator is provided. 
 ABSTRACT: A new Lane relation of fluvial hydraulics is derived from basic principles of sediment transport. It is expressed as follows: Q_{s} (d_{s}/R)^{1/3} ∝ γ Q_{w} S_{o} Unlike the original Lane relation, this new relation is dimensionless. An online calculator is developed to solve the sediment transport equation arising from the new Lane relation. 
 ABSTRACT:
The concepts of Froude and Vedernikov numbers are reviewed on the occasion of the 50th anniversary of the publication of Ven Te Chow's Handbook of Applied Hydrology.
While the Froude number (F) is standard fare in hydraulic engineering practice, the Vedernikov number (V) remains to be recognized by many practicing engineers.
A comprehensive description of the variation of β, the altogether important
exponent of the dischargeflow area rating 
 ABSTRACT: The concept of runoff diffusion is reexamined. Diffusion is inherent to reservoirs and it is always produced in flow through reservoirs. In channel flow, diffusion is produced in the absence of kinematic wave conditions, i.e., under diffusion wave conditions, provided the Vedernikov number is less than 1. In catchment runoff, diffusion is produced: (1) for all wave types, when the time of concentration exceeds the effective rainfall duration, a condition which is usually associated with midsize and large basins, or (2) for all effective rainfall durations, when the wave is a diffusion wave, which is usually associated with a sufficiently mild catchment slope. 
 ABSTRACT: The concept of hydraulic diffusivity and its extensions to the dynamic regime are examined herein. Hayami (1951) originated the concept of hydraulic diffusivity in connection with the propagation of flood waves. Dooge (1973) extended Hayami's hydraulic diffusivity to the realm of dynamic waves. Subsequently, Dooge et al. (1982) expressed the dynamic hydraulic diffusivity in terms of the exponent of the dischargearea rating. Lastly, Ponce (1991) expressed it in terms of the Vedernikov number, further clarifying the mechanics of flood wave propagation. 
 ABSTRACT: Henderson's formulations of the energybased and momentumbased limiting contraction ratios are reviewed (Henderson 1966). Henderson's explicit energybased equation is found to be correct, however, his implicit momentumbased equation is found to be incorrect. A new explicit momentumbased 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 PenmanMonteith combination method for the calculation of evaporation is reviewed and clarified. Unlike the original Penman model, in the PenmanMonteith model the masstransfer evaporation rate is calculated based on physical principles. An illustrative example is worked out to show the computational procedure. An online calculation using ONLINE PENMANMONTEITH gives the same answer. 
 ABSTRACT: This document provides a tabular comparison of several sharpcrested weirs for discharge measurement in openchannel flow. The following weirs are considered: (1) Vnotch, fully contracted; (2) Vnotch, partially contracted; (3) Cipolletti; (4) rectangular; (5) standard contracted rectangular; and (6) standard suppressed rectangular. Descriptions follow the USBR Water Measurement Manual. 
 ABSTRACT: Clark's original unit hydrograph and Ponce's somewhat improved version are explained and compared. Clark's procedure routes, through a linear reservoir, the discrete timeareaderived unitrunoff hyetograph, while Ponce's procedure routes the continuous timeareaderived unit hydrograph. Since the unit hydrograph has a longer time base than the unitrunoff hyetograph, Ponce's procedure provides a somewhat smaller peak discharge than Clark's. The difference, however, does not appear to be substantial. 
 ABSTRACT: The Creager curves are reinterpreted in light of the theory of flood wave diffusion. Experience shows that greater flood wave diffusion corresponds with larger drainage areas. Thus, the trend of the Creager curves admirably reflects the flood wave diffusion that is likely to be present in the real world. 
 ABSTRACT: An online calculator of the ShuttleworthWallace method for calculating evapotranspiration from sparse crops is developed. The method can be used to complement evapotranspiration calculations based on the PenmanMonteith method. 
 ABSTRACT: Gradually varied flow watersurface profiles are expressed in terms of the critical slope S_{c}. In this way, the flowdepth gradient dy/dx is shown to be strictly limited to values outside the range encompassed by S_{c} and S_{o}, in which S_{o} is the bed slope. This new approach improves and completes the definition of flowdepthgradient ranges in the analysis of watersurface profiles. Online calculators are provided to round up the experience. 
