Solomon Seyoum
Learning objectives Upon successful completion of this lecture, the participants will be able to describe: The different approaches for estimating peak runoff for urban drainage network designs Rational method of computing peak runoff and its application, assumptions and limitations Hydrograph method of estimating flow hydrographs for urban drainage network designs such as time area method, unit hydrograph method and kinematic wave method
Hydraulic Design Runoff Runoff estimation for hydraulic sizing of stormwater runoff facilities such as pipe systems, storm inlets and culverts, small open channels, and detention facilities
Hydraulic Design Runoff Many different approaches Statistical analysis of the flood records Regression equations Rational method Hydrograph method
Hydraulic Design Runoff Statistical analysis of the flood records empirical method calibrates a probability model with peak annual discharge observations relates design flow magnitude to frequency directly does not consider rainfall or catchment properties or processes useful where records of more than 20 years runoff data are available at or on the same location near the drainage facility site
Hydraulic Design Runoff Regression equations empirical method use equations previously developed through statistical analysis to predict the peak discharge relate the peak to catchment properties, including area, mean annual precipitation, and slope useful if flood records are not available at or near the project site, or other methods are judged inappropriate
Hydraulic Design Runoff Rational method simple conceptual method estimates peak runoff rate for a selected frequency appropriate for urban and rural catchments less than 80 hectares in which natural or man-made storage is minor relies on an assumption that the design flow of a specified frequency is caused by rainfall of the same frequency best suited to the design of urban storm drain systems
Hydraulic Design Runoff Hydrograph method conceptual method relies on a mathematical representation of the critical processes by which rainfall on a catchment is transformed to runoff used with a design rainfall hyetograph, which specifies the time distribution of rainfall over a catchment computes a runoff hydrograph: the peak flow, time of peak, and corresponding volume can be found
Rational method appropriate for small drainage areas of up to about 80 hectares with no significant flood storage provides peak discharge value not a time series of flow (hydrograph) relates the peak discharge (q, m3/sec) to the drainage area (A, ha), the rainfall intensity (i, mm/hr), and the runoff coefficient (C) q = CiA 360
Rational method runoff coefficient ratio of runoff to rainfall difficult to estimate b/c it represents the interaction of many complex factors, including the storage of water in surface depressions, infiltration, antecedent moisture, ground cover, ground slopes, and soil types. vary with respect to prior wetting and seasonal conditions average values are used for simplicity where a drainage area is composed of subareas with different runoff coefficients, a composite coefficient is used
Rational method Rainfall Intensity a function of geographic location, return period, and storm duration Rainfall intensity at a duration equal to the time of concentration (T C ) is used to calculate the peak flow The rainfall intensity can be selected from the appropriate IDF curves
Rational method Area the drainage surface area in hectares, measured in a horizontal plane, measured from plans or maps using a planimeter or GIS, includes all land enclosed by the surrounding drainage divides,
Rational method Time of Concentration the time it takes for runoff to travel from the most hydraulically distant point in the catchment to the outlet taken as the sum of the overland flow time, t o (or the "time to entry" or the "inlet time"), and the time of travel, t d, in sewers or the main channel must be estimated along all the possible flow paths and the maximum is used
Rational method Time of Concentration t + t + t + t 01 d1,2 d2,3 d3,7
Rational method Time of Concentration t + t + t 02 d2,3 d3,7
Rational method Time of Concentration t + t + t + t 05 d5,4 d4,3 d3,7
Rational method Time of Concentration t + t + t 04 d4,3 d3,7
Rational method Time of Concentration t06 + t d 6,7
Rational method Time of Concentration t 07
Rational method Time of Concentration Inlet time for small fully-sewered areas, some drainage authorities specify t o as a constant typically ranging from 5 to 15 minutes In more complex situations, it is recommended to use the kinematic wave formula t0 = 6.9L n i s 0.6 0.6 0.4 0.3 where t o is inlet time in minutes, L is the travelled length (m), n is the Manning's roughness coefficient, i is the rain fall intensity (mm/hr), and S is the slope of the catchment (m/m).
Rational method - Assumption The rate of runoff resulting from any constant rainfall intensity is maximum when the duration of rainfall equals the time of concentration The frequency of peak discharge is the same as the frequency of the rainfall intensity for the given time of concentration The rainfall intensity is uniformly distributed over the entire drainage area The fraction (C) of rainfall that becomes runoff is independent of rainfall intensity or volume
Rational method - Limitations the assumption of constant rainfall intensities for large catchments is not valid rainfall intensities usually vary during a storm frequencies of peak discharges depend on rainfall frequencies, antecedent moisture conditions in the catchment and the response characteristics of the drainage system, rainfall intensity varies spatially and temporally during a storm the constant runoff coefficient assumption is reasonable only for impervious areas, such as streets, rooftops, and parking lots
Rational method - Limitations for pervious areas, the fraction of runoff varies with rainfall intensity, accumulated volume of rainfall, and antecedent moisture conditions, It limits the evaluation of design alternatives available in urban areas because of its inability to accommodate the presence of storage in the drainage area
Rational method - Application applicable in estimating storm water runoff peak flows for hydraulic designs on very small catchments and small highly impervious areas, design of gutters, drainage inlets, storm drain pipes, culverts and small ditches should not be used for calculating peak flows downstream of major hydraulic structures like bridges, culverts and storm sewers that may act as a restrictions and impact the rate of discharge
Modified Rational Method For higher intensity storms infiltration and other losses have a proportionally smaller effect on runoff The runoff coefficient are usual applicable for 10 year or less recurrence intervals Rational method is modified to account for reduction of infiltration and other loses during high intensity storms C * CiA q = f 360
Hydrograph methods Rational Method provides only peak flow and not a hydrograph, Hydrograph methods overcome this limitation Hydrograph methods used when catchments are large, where storage influences the time distribution of f low, where storage is a part of the design problem
Time area Method Area is treated as a constant in the Rational Method the contributing area is not constant during the beginning of rainfall the area builds up with time uses the time area diagram to produce a flow hydrograph allows straightforward use of time-varying rainfall the design storm The cumulative time-area curve is formed by summing the incremental areas and the corresponding travel times
Time area Method Assumption: time area plot for each individual pipe sub-catchment is linear each pipe is designed considering the flow not only form local sub-catchment but also with the concentrating flows from upstream pipes The combined time area diagram for each pipe can be produced using the principle of linear superposition
Time area Method A A 1 +A 2 A 2 A 1 t d1,2 t c2 t c1 +t d1,2 t
Unit Hydrographs defined as the out-flow hydrograph resulting from a unit depth of effective rain falling uniformly over a catchment at a constant rate for a unit duration D
Unit Hydrographs can be used to construct the hydrograph response to any rainfall event based on three guiding principles: For the same duration of rainfall, the runoff duration is same irrespective of the difference in the intensity; The runoff ordinates are in the same proportions with the intensities of the rainfall; The principle of superposition is valid.
Unit Hydrographs a hydrograph from a complex storm is obtained by adding ordinates of individual hydrographs displaced according to time of origin of excess rain on the catchment i Q D ( ) Qt N = UD (, ji ) m= 1 Q( t ) runoff hydrograph ordinate at time t( m 3 / s ) U( D, j ) D-h unit hydrograph ordinate at time j( m 3 / s ) I m is the rainfall depth in the m th of N blocks of duration D( m) j = t ( m 1 ) D () s m t
Synthetic unit hydrographs unit hydrographs are derived form runoff records, if available because of lack of runoff records, hydrologic design depends on methods of synthetic hydrograph many procedures for synthetic unit hydrographs the SCS dimensionless unit hydrograph is frequently used in the practice t t r p Q p = 0.133* t tr = + 0.6* t 2 p c c 2.08* A = t t r is the effective duration t c is the time of concentration t p is time to peak flow rate, hours A is catchment area in square kilometres Q p is the peak flow rate in m 3 /s
Synthetic unit hydrographs Then once the time to peak t p and peak flow Q p are calculated as above, the SCS dimensionless unit hydrograph is used to calculate the ordinates of the hydrograph t/t p Q/Q p t/t p Q/Q p 0 0 2.6 0.107 0.2 0.1 2.8 0.077 0.4 0.31 3 0.055 0.6 0.66 3.2 0.04 0.8 0.93 3.4 0.029 1 1 3.6 0.021 1.2 0.93 3.8 0.015 1.4 0.78 4 0.011 1.6 0.56 4.2 0.008 1.8 0.39 4.4 0.006 2 0.28 4.6 0.004 2.2 0.207 4.8 0.002
Kinematic wave methods Unit hydrograph methods are empirical approaches various components of runoff generation and movement of runoff are not well understood the complexity of the processes is so enormous that it would be impractical to collect all the required data movement of water over land surface is governed by laws of conservation of mass and of momentum Preferable for small areas with a high percentage of impervious surface
Kinematic wave methods 1 A Local Q t acceleration term + 1 A x Q A Convective acceleration term 2 + g y x Pressure force term g( S o S f Gravity force term ) Friction force term = 0 Kinematic Wave Diffusion Wave Dynamic Wave S o S = f 0 A Q + = Ieff t x Kinematic wave equation
Kinematic wave methods 1 2 Q = M * B* S * y t 5 3 t I = P E S W I eff, t t t t t t y t is determined from continuity equation Where Q t = discharge at time t M = Manning s roughness number B = Flow channel width S = Surface slop y = Runoff depth at time t I eff, t = Effective precipitation t P t = Rainfall depth at time t S = Surface storage loss at time t t I = Infiltration loss at time t t E t = Evapotranspiration at time t W = Wetting loss at time t t dy I, * t eff t A Qt = * A Where A is contributing catchment area dt
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