Sensitivity of Flood Routing Models to Variations of Momentum Equation Coefficients and Terms (HES 41)

unpublishednot peer reviewe

Surcharge of sewer systems

Surcharge of a sewer is the situation in which the sewer entrance and exit are submerged and the pipe is flowing full and under pressure. In this report the hydraulics of the surcharged flow as well as the open-channel flow leading to and after surcharge is discussed in detail and formulated mathematically. The transition between open-channel and surcharge flows is also discussed. This information is especially useful for those who intend to make accurate advanced simulation of sewer flows. In this study an approximate kinematic wave - surcharge model called SURKNET is formulated to simulate open channel and surcharge flow of storm runoff in a sewer system. An example application of the model on a hypothetical sewer system is presented.U.S. Department of the InteriorU.S. Geological SurveyOpe

Hydraulic resistance in alluvial channels

An analytical study was conducted for the determination of the Weisbach resistance coefficient for flow in sand-bed straight channels. Available experimental data were reanalyzed based on dimensional analysis and fluid mechanics concepts. It was found that for flows having width to depth ratio greater than 5, there is a unique and systematic relationship among the Weisbach resistance coefficient f, the Froude number of the flow, and the sediment particle size to hydraulic radius ratio. The bed form which also is a dependent variable is also uniquely determined. For flow with Froude number less than 0.5 where its effect can be neglected, the resistance coefficient can be expressed as a function of the Reynolds number, sediment size to hydraulic radius ratio, and the sediment terminal fall velocity to shear velocity ratio. Application of the results for engineering purposes is also discussed. The technique for engineering applications of the results appear to be quite simple.U.S. Department of the InteriorU.S. Geological SurveyOpe

Spatially varied open-channel flow equations

Recent development and improvement in numerical techniques and computer capability enables more accurate numerical solutions of spatially varied flow problems such as various phases of urban storm runoffs. Consequently, it is desirable to re-examine fundamentally the compatibility of the flow equations used in solving unsteady spatially varied flow problems. To achieve this goal, the continuity, momentum, and energy equations for unsteady nonuniform flow of an incompressible viscous nonhomogeneous fluid with lateral flow into or leaving a channel of arbitrary geometry in cross section and alignment are formulated in integral form for a cross section by using the Leibnitz rule. The resulted equations are then transformed into one-dimensional form by introducing the necessary correction factors and these equations can be regarded as the unified open-channel flow equations for incompressib1.e fluids. The flow represented by these equations can be turbulent or laminar, rotational or irrotational, steady or unsteady, uniform or nonuniform, gradually or rapidly varied, subcritical or supercritical, with or without spatially and temporally variable lateral discharge. Flow equations for certain special cases are deduced from the derived general equations for the convenience of possible practical uses. Conventionally used various equations for open-channel flows are shown to be simplifications and approximations of special cases of the general equations. The inherent difference between the flow equations derived based on the energy and momentum concepts is discussed. Particular emphasis is given to the differences among the energy dissipation coefficient, the frictional resistance coefficient, and the total-head loss coefficient. Common hydraulic practice of using the Chezy, Manning, or Weisbach formulas to evaluate the dissipated energy gradient or the friction slope is only an approximation.U.S. Department of the InteriorU.S. Geological SurveyOpe

Methodologies for flow prediction in urban storm drainage systems

Increasing public concern on urban storm water quantity and quality problems demands a thorough review of the methodologies for flow prediction and design of urban storm drainage systems and development of improved methodologies. In this study the urban storm drainage system is considered as an integrated system of components of urban surf ace, gutters, inlets, sewer branches, junctions, manholes, and other structures. The flow equations that can be used to solve storm drainage problems are critically reviewed and the mathematical methods for solving the St. Venant equations are compared. A method to routing the unsteady flow due to rainfall and other inputs through land, surface and gutter to produce the inlet hydrograph is proposed. The results have been presented in nondimensional form for general uses. A mathematical simulation model for tree-type sewer networks is developed by using the St. Venant equations to route the inlet hydrographs through the network. An overlapping segment scheme is used to account for the backwater effects and mutual influences of the unsteady flow in the sewers. The results show clearly the importance of detention storage in the drainage system and the possibility of detention storage manipulation for flood peak attenuation. In addition to flow prediction purposes, the developed model can also be used for design of sewer systems. Furthermore, new approaches based on risk consideration are proposed for determination of design rainfall and for design of sewers and other hydraulic structures.U.S. Department of the InteriorU.S. Geological SurveyOpe

Illinois storm sewer system simulation model: user’s manual

The Illinois Storm Sewer System Simulation Model is a mathematical model for sewer design and flow prediction utilizing the Saint Venant equations to route unsteady flows through tree-type sewer networks. An overlapping segment scheme is used in the numerical solutions to account for the backwater effects and mutual influences of the sewers and junctions. The program is written in PL/1 and assembler Language and can be executed on most large IBM 360 and 370 systems. User oriented information is provided in this report. An example on sewer design is also given.U.S. Department of the InteriorU.S. Geological SurveyOpe

Incorporation of uncertainties in real-time catchment flood forecasting

Floods have become the most prevalent and costly natural hazards in the U.S. When preparing real-time flood forecasts for a catchment flood warning and preparedness system, consideration must be given to four sources of uncertainty -- natural, data, model parameters, and model structure. A general procedure has been developed for applying reliability analysis to evaluate the effects of the various sources of uncertainty on hydrologic models used for forecasting and prediction of catchment floods. Three reliability analysis methods -- Monte Carlo simulation, mean value and advanced first-order second moment analyses (MVFOSM and AFOSM, respectively) - - were applied to the rainfall -runoff modeling reliability problem. Comparison of these methods indicates that the AFOSM method is probably best suited to the rainfall-runoff modeling reliability problem with the MVFOSM showing some promise. The feasibility and utility of the reliability analysis procedure are shown for a case study employing as an example the HEC-1 and RORB rainfall-runoff watershed models to forecast flood events on the Vermilion River watershed at Pontiac, Illinois. The utility of the reliability analysis approach is demonstrated for four important hydrologic problems: 1) determination of forecast (or prediction) reliability, 2) determination of the flood level exceedance probability due to a current storm and development of "rules of thumb" for flood warning decision making considering this probabilistic information, 3) determination of the key sources of uncertainty influencing model forecast reliability, 4) selection of hydrologic models based on comparison of model forecast reliability. Central to this demonstration is the reliability analysis methods' ability to estimate the exceedance probability for any hydrologic target level of interest and, hence, to produce forecast cumulative density functions and probability distribution functions. For typical hydrologic modeling cases, reduction of the underlying modeling uncertainties is the key to obtaining useful, reliable forecasts. Furthermore, determination of the rainfall excess is the primary source of uncertainty, especially in the estimation of the temporal and areal rainfall distributions.U.S. Department of the InteriorU.S. Geological SurveyOpe

Advanced methodology for storm sewer design—phase II

This report describes further development of computer models for determining the diameter, slope and elevations of each pipe in a storm drainage system in which the layout and manhole locations are specified. The design procedure is based on a least-cost criterion and utilizes discrete differential dynamic programming as the search technique. In this phase of the study a detention storage capability has been added to the model using two approaches. The first approach requires the specification of a maximum allowable outflow and computes the required storage. The second approach determines the storage volume such that the sum of the storage and pipe system costs is a minimum. The procedure for computation of expected damage costs has been changed to reflect the variation of flood damage with flood volume. Also a surface runoff component has been added. This option uses the hydrograph generation portion of the Illinois Urbana Drainage Area Simulator model. Improved cost specification methods as well as flexible pipe elevation constraint capabilities have been added. The new developments are illustrated using two example basins.U.S. Department of the InteriorU.S. Geological SurveyOpe

Advanced methodologies for design of storm sewer systems

This report describes the development of a series of computer models capable of determining the diameter, slope and crown elevations of each sewer in a storm drainage system in which the layout and manhole locations are predetermined. The criterion for design decisions is the generation of a least-cost system. The basis for all of the models is the application of discrete differential dynamic programing (DDDP) as the optimization tool. Two important concepts are introduced as optimal model components: hydrograph routing and risks and uncertainties in designs. Three routing procedures are adopted, each with its own advantages. Expected flood damage costs are evaluated through the analysis of numerous risks and uncertainties associated with the design. This analysis permits the estimation of the probability of exceeding the capacity and the corresponding expected assessed damage of any sewer in the system. The expected damage cost is added to the installation cost to obtain the total cost which is then minimized in the DDDP procedure. Two example sewer systems are used as a basis for illustrating different aspects of the various least-cost design models and developing user guidelines.U.S. Department of the InteriorU.S. Geological SurveyOpe

Illinois least-cost sewer system design model: ILSD-1 & 2 user’s guide

ILSD models are sewer system models for least-cost optimal design of the entire system. ILSD-1 designs for a specified layout the size and slope of the sewers with or without detention storages with user supplied rainfall and/or inlet hydrographs. ILSD-2 is similar to ILSD-1 but also with risk consideration; i.e., with the risk damage cost included in the optimization procedure and a risk equation supplied by the user. The user may choose either ILSD-1 or 2 as he (she) wishes and according to the available data. This user's guide provides the necessary information to use the computer program. Data preparation for various options to fit different engineering situations is presented.U.S. Department of the InteriorU.S. Geological SurveyOpe