360. Online publications featuring online calculations [180514] 
 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. 
