Chapter H. Introduction to Surface Water Hydrology and Drainage for Engineering Purposes

Transcription

1 Chapter H. Introduction to Surface Water Hydrology and Drainage for Engineering Purposes As seen in Figure H.1, hydrology is a complex science that deals with the movement of water between various stages of the hydrologic cycle, and its effects on climate, flora and fauna, and humans. For Civil Engineering purposes, there are many issues such as the amount and timing of runoff, groundwater quantity and quality, pollutant transport, sediment transport and erosion. Engineers are usually concerned with how to manage these aspects and to make sure that they do not adversely impact our activities. For a particular project, we are concerned with one or more of high flows, low flows, or typical flows, depending on the objectives. The scales of hydrology are diverse. For engineering purposes, the small end of the range usually deals with site drainage (e.g. designing a drainage system for a new building). The large end of the scale deals with very large river systems such as the Mississippi, where we need to be concerned with flood stages, low water effects on navigation, sediment transport and accumulation behind dams, pollutant transport, and many other aspects. Hydrology clearly impacts hydraulic engineering in many ways. For the purpose of this introduction, we will only look at one major aspect: stream flows after rain storms. Thus, we will think of surface water hydrology in a very narrow way: how can hydrology provide the input flows that we use for hydraulics and hydraulic design? This topic impacts all building sites, road and bridge design and, most obviously, the design of drainage systems. There are also questions on the FE exam dealing with runoff. Hydrology is a lot more empirical than hydraulics, and relies on observations and generalizations of these observations. You will recognize some hydraulic formulas, often quite simplified from what we have done before. We will make use of the TR-55 Manual for this section of the course. We will cover much taking place in the TR-55 Manual. For the Stormwater Drainage Manual, Chapter 2 looks at rainfall, while Chapter 3 looks at runoff, but we will not cover everything contained in these chapters. The notes here are more of an overview to what we will cover than a complete description for all sections. H-1

2 Figure H.1. The hydrologic cycle. H.1 Surface Water Processes Hydrology as seen here does not have difficult principles but can become very confusing, with many steps and opaque formulas that only work in one set of units. However, there are several main processes that are always at work and act together: 1. Rainfall a. Geographic Location b. Amount/Time/Intensity c. Return Period 2. Site Conditions a. Size/Length b. Gradient c. Soil Type/Vegetation/Development/Moisture Content H-2

3 Together, the rainfall and the site conditions lead to runoff and stream flows that become inputs for our hydraulics and engineering design. There are several different methods that can be used to examine rainfall/runoff that we will divide into two categories: 1. Methods that look at a peak flow/steady state flow, 2. Methods that look at the time variation of flow. Peak/steady-state methods are the simplest, but methods that examine the time variation of stream flows are more powerful and more general. H.1.1 Watershed Delineation Delineating the watershed draining to our site is the first task that must be accomplished. A topographic map or Digital Elevation Model (DEM) is necessary to find the boundaries. There are two main tasks for this: 1. Identify upstream points dividing watersheds (peaks, ridges) 2. Connect these points to form the watershed area (see class examples). Boundaries are perpendicular to contours going up valleys and run along the tops of ridges. This will be the watershed area for the site of interest. If there are manmade structures upstream, the study becomes more complex (e.g. partial flow captured by sewer), but we will not take this into account for this introductory course. H.2. TR-55 Manual The TR-55 Manual, Urban Hydrology for Small Watersheds, is a useful introduction to surface water hydrology and the computation of flows for engineering design. The manual is available online or at the class web site. There is both a paper version of the methodology and a computerbased version, WinTR-55. Because of time constraints, we will only examine the paper version of TR-55. It has two main methods for computing flows: (1) the Graphical Peak Discharge Method, which only computes peak flows and has many assumptions that may limit its use; and (2) the Tabular Hydrograph Method, which computes the time variation of discharge and can be used for more complex environments. H-3

4 For engineering design, the main outputs of these procedures are flow rates that can be used to size channels, design drainage systems and so on. The two main methods both follow the sequence: Rainfall Runoff Flow Rates. This means that a design rainfall then leads to a quantity of surface runoff. This runoff then creates flow rates that may be used for engineering design. There is significant overlap between the two methods, with the main difference being how runoff is translated to flow rates. We will not cover all aspects of the TR-55 Manual, but will learn basics that will allow for computation of design flows for many engineering situations. Parts of these techniques may be used for some of the senior design projects. At the end of the hydrology section, we will also cover the Rational Method, which is not included in the TR-55 Manual. The Rational Method is very simple for designs on small sites, and is almost always on the FE Civil Exam. H-4

5 H.3 Curve Numbers and Runoff H.3.1 Total Runoff Once total rainfall is known (in inches), it is usually useful to know runoff (also in inches). Using inches of runoff might seem strange, but it is independent of watershed area, and may be multiplied by this area to get total runoff volume. Total runoff will not be the same as total rainfall for a storm, as some water is intercepted by vegetation, puddles and other sinks, some makes its way to the groundwater table, and some will go towards replenishing soil moisture. The SCS has methods for this based on Curve Number (CN) that are given in Chapter 2 of the TR-55 manual. According to Eq. 2.1 of TR-55 R = ( P Ia ) ( ) a 2 P I + S (H.1) where R is the runoff, P is precipitation, I a is the initial abstraction (amount of water lost to puddles, vegetation, etc.), and S is the soil moisture deficit. (Not bed slope!) (Note that we have changed the symbol Q in the TR-55 Manual to R so that it is not confused with flow rate.) All quantities are measured in inches. If P I a < 0, then all precipitation is absorbed and there is no runoff. If P I a > 0, there will be runoff that increases nonlinearly. Through empirical methods, it is found that a reasonable approximation for initial abstraction is = 0.2S and so Ia R = ( P 0.2S) 2 P+ 0.8S (H.2) as seen in Figure H.3. The soil moisture deficit is given from the Curve Number as 1000 S = 10 (H.3) CN The curve number is determined by the soil type, vegetation, development, and antecedent runoff condition (ARC), which essentially means the pre-storm soil moisture condition. For a homogeneous watershed, the curve number is just read off Table 2.2 of TR-55. For more complex watersheds, Figure 2-2 of TR-55 provides a flow chart: impervious areas are important here if they differ from assumptions in TR-55 Table 2.2. Once a curve number is determined, the H-5

6 resulting CN may be used to compute the total runoff, R. For these complex watersheds, one of the most important parts of this procedure is the determination of whether impervious areas are connected or unconnected. A connected impervious area outlets directly to the drainage (e.g. gutter), while unconnected impervious areas have flow over pervious areas before entering the drainage system (e.g. parking lot drains to a nearby field). From TR-55 Figure 2-2, these are treated differently. When computing overall CN for watersheds with different types of land use, area-weighted averages are used to obtain a composite CN as seen in Worksheet 2 (Figure 2-5). This overall CN can be used to compute runoff as given in Equation (H.2). Figure H.2. Curve numbers and runoff, using Ia = 0.2S. H.3.2 Runoff from Composite Watersheds When the watershed under consideration has more than one type of land use (which is most of the time), it is necessary to use slightly more sophisticated techniques to estimate an overall curve number. Once the curve number has been found for each different land use type in the watershed, the overall curve number is found as an area-weighted average of all of the individual curve numbers. These are computed on Worksheet 2 and examples 2-1 to 2-4 (Figs. 2-5 to 2-8) of TR-55. Additional blank worksheets are found in Appendix D of TR-55 and on the class website. H-6

7 H.3.3 Incremental Runoff For computing the time history of streamflows (which we have not looked at yet), it is useful to know the incremental runoff produced in a time period (say 0.1 hours). This would seem difficult, but it is actually not that much harder than finding the total runoff. Let us say that we have a simple storm where the rainfall in each hour is given by Table H.1, and the overall curve number is CN=88. This gives a soil moisture deficit of S=1.36 inches. Computing R at every time interval, using the cumulative precipitation P to that point and (H.2), gives a total runoff of 0.51 inches by the end of the storm. The runoff produced during each portion of the storm, R, is simply the difference between runoffs at the various time intervals. This is not difficult, but it gets a little more confusing. The runoffs generated will turn into stream flow, but a runoff of R = generated in 0.1 hours will influence stream flow for much more than 0.1 hours its influence is felt over more like 3 4T c, where T c is the time of concentration to be seen in the next section H.4. The methods to translate this runoff into streamflow are called unit hydrographs, and will be introduced in section H.6, and TR-55 procedures in section H.7. Table H.1. Incremental runoff using Curve Numbers Time (hours) P (inches) R (inches) R (inches) H-7

8 H.4 Site Characteristics All surface water hydrology studies need to know site information. If our design looks at the design flow at a specific point (for example we want to build a small highway bridge at some location) then the first thing we need to know is the watershed (region that drains to that point). Rainfall that falls in this watershed will either drain to our site location, be stored in the watershed, evaporate, or pass through the ground to the groundwater table, which may or may not drain similarly to the surface water watershed. For the purposes of this class, we will only look at small watersheds, where the hydrology is much simpler. Important site characteristics include size (1 acre=1/640 square miles, 1 ha = 10,000m 2 ), length (long, thin watersheds are different from more blocky ones), vegetation (treed, grassy, etc), site development (low density single family housing, farmland), soil type (clay, sandy, ), soil moisture levels before the storm (dry, ), and gradient (ft/mile, m/km). Not all of these will be needed for all analyses and storms. H.4.1 Time of Concentration The time of concentration, T c, is the time for flow from the most hydraulically distant point in a watershed to reach the location considered. It is the most fundamental time scale for the watershed, and strongly affects all estimates of flow rates. Since there may be different paths to the study location, the time of concentration is always the longest time from any subregion. Not all flow will take T c to flow to the outlet of course most points will take less time and thus even if there is instantaneous rainfall (and thus runoff produced instantaneously), streamflow will be spread out much more with time scales of 2-3Tc. There are many different procedures for computing time of concentration. The Indiana Stormwater Drainage Manual gives some in Section These are quite old and there may be some that are more accurate. One common approach is to divide the watershed into sections as shown in Chapter 3 of the TR-55 manual: (1) Sheet flow (over grass, fields, etc), (2) Shallow Concentrated Flow (e.g. gutters), and (3) Open Channel Flow. Sheet flow never exceeds 300ft, and usually is limited to 100ft or less. The time for sheet flow is given by Eq. 3.3 in TR-55: H-8

9 T ( nl) =, (H.4) ( P ) t S0 where T t1 is in hours, n is a Manning s coefficient for overland flow given in Table H.2, L is the length of overland flow in feet (always less than 300ft), P 2 is the two-year, 24 hour rainfall in inches, and S0 is the slope. Table H.2. Manning s n for sheet flow After sheet flow, shallow concentrated flow takes place until some sort of channel is reached. This is also estimated with a simplified equation, and is split between paved and unpaved flows. From the TR-55 manual, Appendix F, V V = S, Unpaved, (H.5) , Paved = S0 L2 where V is the velocity in ft/s. The travel time for this section in hours is then Tt 2 =. 3600V The final travel time uses Manning s equation for bankfull conditions (depth is to top of channel) as we have done before. If there is more than one consecutive channel leading to the point of interest, the travel times are added together. κ 2/3 1/2 L3 V3 = Rh S0, Tt3 = (H.6) n 3600V 3 2 H-9

10 The total time of concentration will then be T = T + T + T (H.7) c t1 t2 t3 Finally, there are some more approximate, simple, equations covering watersheds <200 acres (From Houghtalen et al., Fund. Hyd. Eng. Sys, 4 th Ed.) T c ( S + 1) L = (H.8) ( S *100) 0 where T c is in hours, L is in feet, S is the soil moisture deficit in inches. H-10

11 H.5 Rainfall Rainfall is a lot more complex than you would expect, and our knowledge is entirely driven by measurements around the country and around the world. Rainfall is complicated by the fact that, for a given site, it can have up to four major components: (A) Total amount (usually in inches) or intensity (inches/hour); (B) Duration (minutes, hours); (C) Frequency (1 in 10 year storm, etc); and (D) Variation in time. The specifics of design rainfall will change from site to site, for changing storm duration and frequency, and for changing site characteristics. H.5.1 Design Hyetographs Measurements give rainfall over time and can be converted into representative curves of rainfall vs time called hyetographs. They are given by several agencies: Figure H.3 shows examples of rainfall fraction vs time for a 24 hour storm as given by the Natural Resource Conservation Service (NRCS, used to be SCS) in the TR-55 Manual. The four different curves show representative rainfall patterns for different parts of the country as given. To find the actual rainfall for a storm using these curves, multiple the total rainfall (usually in inches) by the fraction of rainfall on the curve (vertical axis). Figure H.3. Temporal Variation of Rainfall for 24 hr storm from SCS (now Natural Resource Conservation Service, NRCS) in different parts of the USA. H-11

12 In the Indiana Stormwater Drainage Manual, many more rainfall curves are given in Tables The many types of curves can vary in the time they are valid for (6 hr, 24 hr), the quartile of the storm that sees the maximum intensity of rain (First quartile=i, Second quartile=ii ) and the Huff probability level (percent exceeded in x% of storms). Often we use just some of these for design purposes (50% Huff ordinate ). The first quartile curves are often used for storms less than or equal to 6 hours, second quartile curves are for greater than 6 hours up to and including 12 hours. The third and fourth quartile curves are usually used for maximum durations of more than 12 and less than or equal to 24 hours, and the fourth quartile curves are for storms longer than one day. Note that TR-55 always uses the 24 hour rainfall storm, which becomes increasingly less representative as watersheds become smaller. H.5.2 Design Rainfall Magnitudes of rainfall at a given location also come from statistical analysis of past rainfall events. In TR-55, 24-hour rainfall magnitudes are given in Tables B-2 to B-8 for 2-year to 100- year return periods. For example, South Bend has a 3.9 inch 10-year 24-hour design rainfall in Figure B-5. (10-year means that on average, this will be exceeded once every 10 years). If other times (1 hour, etc.) are desired, they may be found on, for example, the NOAA Precipitation Frequency Data Server Following this to the station on the Notre Dame Campus (Moreau Seminary) gives a 10-year, 24-hour rainfall of 4.08 inches, which is close to the TR-55 value, and a 100-year, 24-hour rainfall of 6.25 inches. The return period may be specified by the project: a small parking lot might have a 10-year return period for drainage, while an interstate design return period might be much larger. Rainfall for steady-state type discharge models is not time-varying but is instead represented as a 3D intensity-duration-frequency curve at some site location. For a given time of storm and return period, the intensity (inches/hour) is given, which is then used as input into the discharge models. These are also given on the NOAA Precipitation Frequency Data Server and the Moreau Seminary 10-year 24-hour intensity is inches/hour which, when multiplied by 24 hours, gives the identical 4.08 inches. However, these intensity-duration-frequency curves are generally not used for 24-hour rainfalls, but for small watersheds (<200 acres) and short rainfall events. H-12

13 H.6 Hydrographs A hydrograph is a record of stream or river discharge over time as seen in Figure H.4. During, and possibly after, a storm the hydrograph will rise quickly to a peak and then recede more slowly. In permanent streams, there will be a base flow before and after the storm and the storm hydrograph is the portion over the base flow (we will not worry much about how to separate them). For many engineering drainage projects on small sites, there will be no base flow (normally dry). The storm hydrograph will be a function of the total precipitation, the length and pattern of precipitation, and the site conditions. Larger sites have runoff that is more spread out over time, as would be expected. Figure H.4. Storm hydrograph, and separation from base flow. For streamflow prediction, the most important aspect is that hydrographs are assumed to behave linearly with runoff as shown in Figure H.5 (Not linear with precipitation!!) Doubling runoff produced over a constant time interval (say from 1 inches to 2 inches) will double the streamflow. Hydrographs are also assumed to superpose, that is to say, streamflow from 1 inch of runoff over two consecutive periods (say 0.1 hours each) will simply be the streamflow from the hydrograph at time hours added to the same hydrograph shifted in time by 0.1 hours. H-13

14 Figure H.5. Linearity and superposition in hydrographs. H.6.1 Unit Hydrographs, Composite hydrographs, and Synthetic Unit Hydrographs These assumptions (which are not entirely true but are close enough for hydrology) lead to the concept of the unit hydrograph. A unit hydrograph is a hydrograph generated by a unit runoff (1 inch or cm) generated over a specific time interval (often the time to the hydrograph peak/10, 0.1T p ). Knowledge of the runoff generated during this time then leads to the construction of a composite hydrograph from the individual unit hydrographs. This can be illustrated with the previous example of incremental runoff. Let us say that for a particular site, the unit hydrograph for a runoff period of 0.1 hours is as shown in Table H.4 (this is a very simple hydrograph: real ones are more detailed). Table H.4. Example Unit Hydrograph Time (hr) Flow (cfs) Applying this unit hydrograph to the runoff generated in Table H.1 gives Table H.5 and Figure H.6. It is constructed by multiplying the runoff generated at a particular time by the unit hydrograph shifted to begin at that time. The hydrographs will overlap, and then are added together to give the total composite hydrograph. Thus, a knowledge of the unit hydrograph and the runoff generated over time can give estimates of streamflow for any design storm. This allows the designer to test different design and rainfall scenarios. H-14

15 The question now becomes: how do we obtain a unit hydrograph? The most direct way is to perform long-term rainfall and streamflow measurements, but this is unrealistic in most cases. Additionally, engineering projects will change the watershed characteristics, which means that historical measurements will be inaccurate for the new conditions. For these reasons, synthetic unit hydrographs have been developed based on the characteristics of the watershed. The NRCS (SCS) has developed synthetic unit hydrographs that are widely used in hydrologic analyses. These unit hydrographs depend on two variables: time of concentration and drainage area, and peak flow rate, q p, is given by: ( ) / q = K A T (H.9) p p p where q p is in cfs, A is the drainage area in square miles, T p is the time to peak flow in hours, and K p is an empirical constant that is usually taken as 484. The time to peak flow is usually taken to be T = 0.67T. The unit hydrograph is then taken found by multiplying the SCS p c dimensionless unit hydrograph axes, seen in Table H.5 below, by T p and q p. Once the unit hydrograph is constructed, the overall streamflow may be found by applying the time-varying runoffs to the unit hydrograph and adding them together. Figure H.6. Construction of a composite hydrograph. Top: unit hydrograph; bottom: individual hydrographs from incremental runoff, and composite hydrograph sum. H-15

16 Table H.5. Construction of a composite hydrograph from runoff and unit hydrograph Time (hours) R (inches) Flow Rates (cfs) Total Table H.6. Dimensionless unit hydrograph and mass curve coordinates for the SCS synthetic unit hydrograph. H-16

17 H.7 TR-55 Tabular Hydrograph Method The full rainfall-runoff-unit hydrograph-composite hydrograph is very long and has many places where people can go wrong. The TR-55 manual provides two simplified methods for computing streamflows. The first we will look at is a simplified method for constructing composite hydrographs. It uses curve numbers to compute runoff (Chapter 2 of TR-55), and 24 hour rainfalls only (Appendix B of TR-55). It is useful for watersheds up to 2000 acres. The Tabular Hydrograph Method will give good results for watersheds that are not homogeneous and match the assumptions (e.g. no significant sewer flow). It is far less complex than full unit hydrograph methods, and can easily be computed by hand. On the downside, it is probably less accurate than more complex hydrograph and other routing methods, as it rounds off quantities and is in fact derived from curve-fits of these methods. The Tabular Hydrograph Method essentially precomputes unit hydrographs (in units of csm or 3 ft 1 1 cubic feet per second per mile area per inch runoff: ). These are done for set times 2 s mile in Ia of concentration, T c, travel times, Tt, and ratios of Initial Abstraction to Precipitation, P (remember Ia = 0.2S). Different rainfall types (I, Ia, etc.) have different tabular hydrographs. For each subregion, the flow for that region is then given by Q= qar (H.10) t m where Q is the flow in cfs (note that in the manual, this is listed as q), A m is the area in square miles (1 mile 2 =640 acres), and R is the runoff in inches (in the manual this is given as Q). The flow from each subregion is then added together to get the total flow like a regular unit hydrograph. There are a few additional things to understand before these can be computed. H.7.1 Travel Times In addition to the time of concentration and runoff, travel times t T are required for nonhomogeneous watersheds where runoff may travel through one type of area (say fields) before traveling downstream through another type of area (say single family subdivision). The travel time through a channel in that subdivision is needed to get an accurate estimate of the overall discharge downstream. For example, in Figure H.7, the travel time corresponding to subarea 1 (upstream part) will be the time to travel through the main stem of subarea 2 (A to B). The travel H-17

18 time T t is found in much the same way as the time of concentration (Chapter 3 of TR-55), but only using Manning s equation for open channel flow and not sheet flow or shallow concentrated flow. This travel time takes into account the additional time to travel through a subregion, and also the spreading out of the flow that will occur along this route. H.7.2 Use of Precomputed Unit Hydrographs There are numerous quantities that must be found before the hydrographs can be used, but these are now all known to us. For each subarea it is necessary to know the area (square miles), the time of concentration (hours), the travel time (hours), the curve number CN, and the 24 hour rainfall total (inches). The downstream subarea (if any) must also be recorded so its travel time may be added. This is done in Worksheet 5a of TR-55. There is one complexity. Because the Time of Concentration, Tc, Total Travel Time Tt, and ratio of Initial Abstraction to Precipitation, Ia / P, are all given as discrete quantities in the tabular hydrographs of Exhibit 5, the raw quantities will not match the tables. Thus, they must be rounded to the nearest values. For Ia / P, this is easy and just round to the nearest value in the table (e.g. if Ia / P= 0.22, round to 0.3 as this is the closest value). For Tc and Tt, the procedure is slightly more complex. Three cases must be considered: 1. Round Tc and Tt separately to the nearest table value, 2. Round Tc down to the nearest table value and Tt up to the nearest table value, 3. Round Tc up to the nearest table value and Tt down to the nearest table value. For each case the sum of Tt and Tc must be computed: whichever case gives the closest match to the raw values should be used. Table H.7 gives an example. For a time of concentration Tc=0.67 hours, the closest tabular values are 0.5 and 0.75 hours (from Exhibit 5). For travel times of 0.22 hours, the nearest tabular values are 0.2 and 0.3 hours. Table H.7 gives results from the three cases. For this example, Case 3 (round up Tc, round down Tt) gives the closest match to the total time of 0.89 hours, so these values should be used from the Tabular Hydrographs. H-18

19 Table H.7 Example Selection of Tc and Tt Actual Case 1 Case 2 Case 3 Tc Tt Total Figure H.7. Example watershed with two subareas, each with a stream. The travel time for water from Subarea 1 flowing through Subarea 2 is added onto the time from the unit hydrograph. Once this is done use Worksheet 5b to record the flow rate contribution from each hydrograph given from equation (H.10). The times on the tabular hydrographs will exceed the number of columns on the Worksheet, so pick a point around 5 or 6 time intervals before the peak flow for the largest area, and start the hydrograph there. Make sure to choose the appropriate rainfall type (I, Ia, II, III), Time of concentration, Travel Time, and Ia/P for each subarea. Use one subarea for each row. When all rows have been completed, sum up the columns to get the total flow rates for the watershed at each point in time. These will give the flow rates around the peak of runoff, but will not give the entire record. If the entire record is needed (for example if complex flood routing is performed downstream), then other methods will need to be used. H-19

20 H.8. TR-55 Graphical Peak Discharge Method If the watershed of interest is homogeneous enough that it can be represented by a single curve number with CN>40, has only one main stream, and is within the allowable range of precipitation values, then the TR-55 peak discharge method of Chapter 4 is an easy way to compute peak discharge with no hydrographs whatsoever. Needed data are: 1. Drainage area (mi 2 ) 2. Runoff Curve Number 3. Time of Concentration (hours) 4. Rainfall Type Distribution (I, II, etc.) 5. Pond and Swamp Areas (percent) hour rainfall amount (inches) The peak discharge Qp (ft 3 /s) is given by Q = q A RF (H.11) p u m p 3 ft 1 1 where q u is the unit peak discharge ( 2 s mile in ), A m is the area in square miles, R is the runoff in inches, and F p is the pond and swamp adjustment factor. After calculating Curve Numbers, Initial Abstractions, and so on, simply and complete worksheet 4 of TR-55. You will need to look up the unit peak discharge in Exhibits 4-I to 4-III and possibly apply a pond and swamp adjustment factor found in Table 4-2 of TR-55. It is very simple, but has significant restrictions and cannot be used for everything. H-20

21 H.9 TR-55 Storage Volume for Detention Basins Imagine that we have just computed the change in peak discharge arising from a planned development. Post-development discharges can be significantly greater than those from predevelopment times, and downstream communities and channels may suffer significant damage. Often, the best way to mitigate these effects is by using detention ponds to temporarily detain water which will spread the overall discharge over time. There are complex storage routing procedures that will do this but often simple estimates are helpful, particularly with small projects. The TR-55 storage volume methodology does this quickly and easily. This only requires two inputs: the Rainfall type (I, Ia, etc.) and the ratio of peak outflow discharge to peak inflow discharge, qo / q p. The ratio of storage volume (Vs) to runoff volume (Vr) may then be read directly off the graph. There is only one small complexity in that storage volumes are usually given in acre feet, while runoff volumes will be in mile 2 inches. These may be converted using V r = RA (H.12) m where R is in inches and Am is in square miles. This may be computed on Worksheet 6. If the Volume-Elevation relationship is known for the detention basin, the TR-55 method can also be used to help design outlet weirs. For a known storage volume, the weir elevation is read off the elevation-volume curve. This is taken as the design water level. If the detention pond is dry (no normal water), the weir crest will then be at the elevation where storage is zero. The weir width may then be solved for directly. More complex weir designs may also be attempted for several different design flows as in class, or in the manual. These can be important because design of a weir for only one design flow may pass too much or too little flow downstream for other design flows. These lead to multiple stage weirs or other compound outlets. Often, these have the form of a narrow weir at low elevations, and a wider weir at higher elevations. These could be both rectangular, or triangular for low flows and rectangular for high flows. However, we will not look at these more complex designs closely in this course. Finally, detention pond volumes are approximate and if an error of 25% in storage can not be tolerated, other methods should be used. H-21

22 H.10 Rational Method On the very small scale, usually taken as less than 200 acres, there are even simpler techniques for computing peak runoff for design purposes. The Rational Method, which is almost always on the FE exam, is given by Qp = CIA (H.13) where Q p is the peak flow in acre-in/hr or cfs (because 1cfs is almost exactly equal to 1 acrein/hr), C is a runoff coefficient, I is the rainfall intensity in inches/hour, and A is the area in acres. Note that this equation may also be used in any consistent set of units (but will require unit conversions, particularly for rainfall). Runoff coefficients are only a function of land use and soil types, as seen in Table H.6. Areas are taken from the watershed drainage (which might be quite small when considering, for example, surface water drainage from one street of a subdivision or for a new building site). Rainfall intensities are taken from Intensity-Duration-Frequency (IDF) curves that are specific to a given location. These may be found on the NOAA Precipitation Frequency Data Server or other sites. This rainfall intensity has two components that must be selected: Frequency (return period of one year, ten years, ) and Duration (5 minute, 10 minute, ). Once these have been determined, the intensity is read off the curve or the table. The precipitation frequency (or return period) is determined by the type of design and the appropriate building codes for a particular location. The storm duration is taken to be equal to the time of concentration, T c, as determined by normal methods, or as specified by local ordinances (e.g. regulations specify that a ten minute Time of Concentration must be used). For non-homogeneous watersheds, the runoff coefficient, C, is area-weighted according to the various land uses. H-22

23 Table H. 6. Runoff Coefficients for the Rational Method. H-23