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Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 3 CHAPTER 4 APPLICATIONS OF HYDROLOGY AND CONCE...

Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 3 CHAPTER 4 APPLICATIONS OF HYDROLOGY AND CONCEPTS OF PROBABILITY AND STATISTICS TO HYDROLOGY APPLICATIONS OF HYDROLOGY 4.1 Design Flow Computation and Pipe Capacity for Storm Sewers A Storm Sewer is a drainage system designed to carry excess surface water, typically from rainfall, away from streets, parking lots, and other paved areas to prevent flooding. Unlike sanitary sewers, which carry wastewater from homes and businesses to treatment plants, storm sewers transport rainwater (and sometimes melted snow) directly into local water bodies, such as rivers, lakes, or retention ponds, without treatment. Storm sewers usually consist of a network of underground pipes, drains, inlets, and manholes that collect and convey stormwater runoff efficiently, reducing the risk of water accumulation on streets and urban surfaces. Storm sewers are essential infrastructure components designed to manage excess water resulting from rainfall and storm events. These systems prevent flooding, protect urban areas, and ensure safe water disposal into natural water bodies such as rivers or lakes. The design of storm sewers involves two critical aspects: design flow computation (estimating the volume of runoff) and pipe capacity determination (ensuring the pipes can handle the runoff efficiently).  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 4 Design Flow Computation Design flow computation refers to calculating the volume of water (runoff) that the storm sewer system needs to handle during a storm event. This step is crucial to ensure that the sewer system can accommodate the expected amount of water without causing flooding or overflow. The runoff depends on factors like: Rainfall intensity and duration: The amount of rain that falls over a specific period, often derived from local Intensity-Duration-Frequency (IDF) curves. These curves help estimate the intensity of a storm based on its frequency (e.g., a 10-year storm) and duration (e.g., 1 hour). Drainage area: The size of the catchment area (or watershed) that drains into the sewer. The larger the area, the more water needs to be managed. Land use and runoff coefficient (C): Different surfaces (like asphalt, concrete, or grass) affect how much of the rainfall turns into surface runoff. Urbanized areas with many impervious surfaces have a higher runoff coefficient, meaning more rainfall turns into runoff. In contrast, natural areas absorb more water, resulting in lower runoff.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 5 RATIONAL METHOD The Rational Method is a simple and widely used formula for estimating the peak discharge (or flow rate) of stormwater runoff from a small drainage area during a specific storm event. It is particularly useful for urban stormwater design in areas less than approximately 80 hectares (200 acres). The method assumes that the rainfall is evenly distributed over the drainage area and that all of the runoff occurs as a direct result of the storm. The Rational Method is expressed as: Where: Q = Peak discharge (m³/s or L/s), or the amount of runoff expected from a storm event. C = Runoff coefficient (dimensionless), which represents the fraction of rainfall that becomes surface runoff. It depends on land use and surface type (e.g., impervious surfaces like roads and buildings have a higher C than natural, grassy areas). i = Rainfall intensity (mm/h or in/h), the rate at which rainfall occurs, typically based on local rainfall data for a specific duration (e.g., 10- minute or 1-hour storm). A = Drainage area (ha or m²), the size of the area contributing runoff to the storm sewer.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 6 SCS-Runoff Method - U.S Soil Conservation Service developed this method. By this method the volume and peak of the runoff can be estimated for a 24-hr design storm. This method can be used for both urban and non- urban small watersheds. - The SCS method uses a dimensionless unit hydrograph and drainage inputs to determine flow volumes and peak discharges.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 7 SCS runoff equation is given as: Modified Rational Method - Modified rational method is an extension of the rational method for rainfalls lasting longer than the time of concentration and the hydrograph. - The basic equation for the Modified Rational Method is: Qp=kCia RUNOFF COEFFICIENT C C is the most difficult variable to accurately determine in the rational method. The fraction of rainfall that will produce peak flow depends on:  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 8 Impervious cover - any type of human-made surface that doesn’t absorb rainfall. Slope - a rising or falling surface. Surface detention - The portion of the storm rainfall that flows on the land surface toward the channel but has not yet reached it. Interception - the capture of precipitation above the ground surface. Infiltration - the process by which water on the ground surface enters the soil. Antecedent moisture conditions - the relative wetness or dryness of a sewer shed, which changes continuously and can have a very significant effect on the flow responses in these systems during wet weather.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 9 Rainfall Intensity (i) I : rainfall rate in in/hr i is selected based on rainfall duration and return period – duration is equal to the time of concentration, tc. return period varies depending on design standards tc = sum of inlet time (to) and flow time (tf) in the upstream sewers connected to the outlet  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 10 PIPE CAPACITY FOR STORM SEWERS - to determine the value use Manning Equation. Manning Formula is used for: To find out the velocity of water in open channel To find the slope of pipe To find out the velocity of water in close channel To find out the pump of flow rate Open Channel This is a flow-through channel that is open to the atmosphere and has free surface; the flow is produced because of gravity that is obtained by providing a bed slope.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 11 Pipe Flow Pipe flow is a flow that takes place under pressure force. In close flow or in close pipe close flow, the pipe has no free surface. Open Channel vs. Pipe Flow Atmospheric pressure at free surface Gravity flow Roughness varies Any shape Velocity varies No free surface Pressurize flow Roughness depends on material of pipe  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 12 Circular Velocity is marls at center STORM SEWER - The capacity of storm sewers depends on various factors, including the size and shape of the pipe, slope, material, and the design specifications. Storm sewer systems are designed to handle the flow of rainwater and prevent flooding in urban areas. The capacity is typically expressed in terms of flow rate, often measured in cubic feet per second (Cfs) or cubic meter per second (Cms).  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 13 PIPE CAPACITY FOR STORM SEWERS Assumption: pipe is flowing full under gravity Sample Problem 1: A drainage area of 5 acres with a runoff coefficient (C) of 0.3. The rainfall intensity (i) for a 1-hour storm is 4 inches per hour. Calculate the peak discharge (Q). Given: Area (A) = 5 acres = 217,800 ft² (since 1 acre = 43,560 ft²) Runoff coefficient (C) = 0.3 Rainfall intensity (i) = 4 inches/hour = 0.33 ft/hour (since 1 inch = 1/12 feet)  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 14 Solution: Q = CiA = 0.3 x 0.33 x 217,800 = 21,534 ft³/hr = 21,534 ft³/hr / (1 hr/3600 sec) Q = 5.98 cfs Sample Problem 2: A residential drainage area of 3 acres has a runoff coefficient (C) of 0.5. The rainfall intensity (i) for a 1-hour storm is 3 inches per hour. Calculate the peak discharge (Q). Given: Area (A) = 3 acres = 130,680 ft² (since 1 acre = 43,560 ft²) Runoff coefficient (C) = 0.5 Rainfall intensity (i) = 3 inches/hour = 0.25 ft/hour (since 1 inch = 1/12 feet) Solution: Q = CiA = 0.5 x 0.25 x 130,680 = 16,335 ft³/hr = 16,335 ft³/hr / (1 hr/3600 sec) Q = 4.45 cfs  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 15 4.2 Flood Plain A floodplain is a flat area of land adjacent to a river or stream that stretches from the banks of its channel to the base of the enclosing valley walls. This region experiences periodic flooding during times of high discharge when the river overflows its banks. Floodplains play a significant role in managing water flow during floods, absorbing excess water, and reducing the impact on downstream areas. They include two main components: the floodway and the flood fringe. Floodway: This is the channel of the river and the adjacent areas that actively carry floodwaters downstream. It’s crucial for controlling water movement during floods. Flood Fringe: These are the areas of the floodplain that are inundated by floodwaters but do not experience a strong current. They serve as overflow areas that can hold excess water.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 16 In simple terms, a floodplain is an area near a river or a stream that floods when water levels rise. Formation of Floodplains Floodplains are formed through two primary processes: 1. Erosional Floodplain: An erosional floodplain is created as a stream cuts both vertically and laterally into its channel and banks. This process gradually carves out the landscape, forming a wide, flat area adjacent to the watercourse. 2. Aggradational Floodplain: Aggradation refers to the increase in land elevation due to the deposition of sediments. When a river has a greater supply of sediments than it can carry, these sediments accumulate, raising the level of the floodplain. This is common in areas where water velocity decreases, causing sediments to settle. Floodplain Mapping Floodplain maps are essential tools in flood risk management. These maps illustrate the areas of land that are prone to flooding during heavy rainfalls or snowmelts, particularly for regions susceptible to seasonal storms. They highlight hazardous zones near rivers, streams, lakes, coastal areas, and other bodies of  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 17 water. Understanding these maps is critical for urban planning, disaster preparedness, and mitigating potential flood damage. The 100-Year Flood A 100-year flood is a flood event that has a 1% probability of occurring in any given year. This term is often misunderstood, as it does not mean the event will only occur once every 100 years; rather, it represents a statistical chance of such a flood happening in any given year. The 100-year flood is also known as the 1% annual exceedance probability flood. It is typically expressed as a flow rate in a river or stream, and the corresponding water level can be mapped to show areas of inundation. Estimating a 100-year flood is often done using stream-gauge records, regional frequency methods, or hydrological models that apply rainfall data to predict the water flow and levels. This information is crucial for creating the 100- year floodplain map, which informs building regulations, environmental policies, and flood insurance requirements. 100-Year Floodplain The 100-year floodplain refers to the area surrounding a floodplain that has a 1% chance of flooding in any given year. This zone is particularly important for development and zoning decisions, as it represents a high-risk area for flooding.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 18 Importance of Floodplain Mapping Floodplain mapping serves several critical functions: Risk Awareness: It shows where flooding is likely to occur, enabling individuals and communities to take preventive measures. Flood Risk Management: Maps help identify the most effective strategies to manage flood risks and develop plans to address potential flooding. Emergency Response: Local authorities and emergency responders use these maps to prepare for and respond to flood events. Urban Planning: Floodplain maps guide development decisions, helping to avoid unnecessary construction in high-risk flood areas, which reduces potential damage and costs. The precision of floodplain analysis is influenced by the terrain's slope. For example, on a steeply sloping floodplain, a small rise in water levels may only flood a limited area, whereas on a relatively flat floodplain, the same rise could inundate a much larger region.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 19 Floodplain Mapping Techniques Floodplain mapping techniques can be classified into two main categories: dynamic and static. 1. Dynamic Techniques: These involve continuous monitoring of river or stream flow and require extensive fieldwork and long-term data collection. Methods such as regression analysis and hydrological modeling fall into this category. They are useful for calculating the frequency of flood events and understanding flood-level characteristics, which are crucial for assessing the risks of development in flood-prone areas. 2. Static Techniques: Static techniques utilize satellite imagery and other data to create floodplain maps at specific points in time. While they may not provide a long-term view of flood patterns, they are valuable for preliminary flood hazard assessments. These techniques are often used when dynamic data is unavailable, combining historical flood data with other resources to estimate flood risks. Both dynamic and static techniques provide essential data for hydrologists and urban planners, helping to develop effective flood management strategies and disaster preparedness plans. Floodplains are vital components of the natural landscape, serving as buffers that mitigate the impact of floods by absorbing excess water.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 20 Understanding their formation, the factors contributing to flood events like the 100-year flood, and the importance of accurate floodplain mapping is crucial for sustainable development and risk management. Through proper floodplain management and mapping techniques, communities can minimize the risk of flood damage, protect lives and property, and ensure safer urban planning and development. 4.3 Spillway Design Spillways are critical structures designed to safely release excess water from reservoirs, typically constructed near or as part of a dam. They serve to prevent overtopping and potential dam failure by controlling the flow of water downstream. Properly engineered spillways are essential to maintain the structural integrity of dams and ensure flood control. Purpose of Spillways Every reservoir has a finite storage capacity. When a reservoir reaches full capacity and additional floodwaters enter, the water level will rise, potentially leading to overtopping. Spillways are implemented to safely direct excess water to downstream areas, usually the river on which the dam is built. These can be either part of the dam structure or located separately, depending on design requirements.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 21 Controlled vs. Uncontrolled Spillways Controlled Spillways: Equipped with gates that can be raised or lowered to regulate water flow. This flexibility offers advantages during flood events, as operators can control the discharge rate. Uncontrolled Spillways: These allow water to overflow automatically when the reservoir reaches a certain level. They lack gates, which makes them simpler but less adaptable.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 22 Spillway as a Safety Measure Spillways act as safety valves for dams, preventing structural failure caused by excessive water pressure. They are necessary to mitigate the risks posed by overtopping, which could otherwise result in dam collapse and downstream flooding. Spillway Location Spillways can be strategically placed based on site conditions and dam structure: Within the dam body: Some designs integrate spillways directly into the dam structure. Side of the dam: Spillways may also be placed at one or both sides of the dam. By-pass spillway: Separate from the dam itself, this type of spillway allows for excess water to be diverted around the dam. Requirements for an Effective Spillway 1. Capacity: The spillway must be capable of handling the maximum expected floodwater discharge. 2. Hydraulic and Structural Adequacy: It must withstand the hydraulic forces and be structurally sound.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 23 3. Safe Disposal: The design should ensure that water is safely carried away from the dam. 4. Erosion Resistance: The bounding surfaces should resist erosion caused by high-velocity water flow. 5. Energy Dissipation: Adequate energy dissipators must be provided downstream to manage the kinetic energy of water exiting the spillway. Types of Spillways 1. Based on Purpose Main (Service) Spillway: Designed to manage regular flood events, this is the primary spillway in most dam designs. Auxiliary Spillway: Functions as a backup, operating only when the main spillway exceeds its capacity. Emergency Spillway: Activated during extreme emergencies to prevent dam failure. 2. Based on Control Controlled (Gated) Spillway: Features gates to regulate the outflow. Uncontrolled (Ungated) Spillway: Lacks gates, allowing water to flow freely once the reservoir reaches a certain level.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 24 3. Based on Design Features Open Channel Spillway: Common in dams like Pantabangan and Caliraya, these use open channels to convey water downstream, relying on the principles of open-channel flow. Also known as chute or trough spillways. Drop Spillway: Used in low dams or weirs, this design allows water to fall freely and almost vertically. Protection from scouring is achieved through an apron or a downstream water cushion. The ogee spillway, found in dams such as Pantabangan Auxiliary Dam and Ambuklao, is a variation of the drop spillway.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 25 Siphon Spillway: Utilizes the difference in height between the intake and outlet to create a pressure difference, aiding in water removal. It requires priming to function correctly.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 26 Bell Mouth Spillway: Characterized by its inverted bell shape, it allows water to enter from all sides, directing it downward. This design is often referred to as a morning glory or glory hole spillway. Spillways are a fundamental component of dam design, ensuring that reservoirs can manage floodwaters effectively and safely. Whether controlled or uncontrolled, their purpose is to maintain the structural integrity of dams while preventing floods downstream. Through careful design, they mitigate the risks associated with dam overtopping and preserve both human lives and property.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 27 CONCEPTS OF PROBABILITY AND STATISTICS TO HYDROLOGY 4.4 Design Storms and Design Runoff DESIGN STORM - represents a hypothetical weather scenario created to assess the possible effects of severe weather on infrastructure and systems. It involves modeling heavy rainfall or other extreme conditions to determine how well structures such as buildings, roads, and drainage systems can cope. This concept is essential for designing infrastructure that remains durable and safe during intense weather events. A precipitation defined for use in the design of a hydrologic system. design frequency/return period is determined first then the design storm needs to be analyzed Analysis of Design Storm 1. Storm Selection: This step involves choosing a storm event that represents the design frequency or return period (e.g., a 25-year or 100-year storm). The characteristics of this storm are used to assess the infrastructure’s ability to handle that level of rainfall. 2. Rainfall Duration Selection: Rainfall duration refers to the period over which the rain occurs during the storm. This is crucial for hydrologic design because the duration influences how much runoff is generated. Short,  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 28 intense storms may lead to flash floods, while longer storms produce different water flow patterns. The duration should reflect local weather patterns and the type of infrastructure being designed. 3. Point Rainfall Depth: Point rainfall depth is the total amount of rain that falls at a specific location during the storm. It is usually obtained from historical weather data and helps in estimating runoff and determining drainage needs. 4. Areal Depth Adjustment: Since rainfall can vary across a region, the areal depth adjustment corrects for differences between rainfall at a single point and the average rainfall over a larger area. This adjustment is important for large regions where the storm's intensity may not be uniform. 5. Time and Areal Distribution of Rainfall: This involves understanding how rainfall intensity changes during the storm (time distribution) and how the rain is spread across the region (areal distribution). Time distribution helps in planning for peak flows, while areal distribution ensures that regional rainfall variations are accounted for in the design. 1. Storm Selection  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 29 Historic Storms: The process starts by examining past storm events, using historical data to identify storms that brought significant rainfall. Flood Data: Information on previous floods is also reviewed to understand the impact of past storms on the region, ensuring relevant storm events are considered for infrastructure design. Rainfall Threshold: A minimum rainfall threshold is set, determining the lowest amount of rainfall required for a storm to be included in the analysis. Storm Selection Criteria: Only storms with daily rainfall amounts equal to or greater than this threshold are selected for further evaluation, focusing on storms that pose real risks to the area. 2. Rainfall Duration Selection Depends on Watershed Size: The duration of rainfall to be used in the design process is influenced by the size of the watershed. Larger watersheds may require longer rainfall durations to account for the time it takes for water to flow across the area. Time of Concentration (tc): This refers to the time it takes for runoff from the farthest point in the watershed to reach the outlet. When rainfall is uniformly distributed, the entire watershed contributes to the peak discharge once this time is reached.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 30 Variable Rainfall Intensity: If the intensity of rainfall changes over time, a duration longer than the time of concentration (tc) is selected to ensure the analysis captures the full impact of the storm. 3. Point Rainfall Depth A HYETOGRAPH SPECIFYING THE TIME DISTRIBUTION OF PRECIPITATION ○ Annual maximum precipitation for a given duration is selected for all storms in a year. ○ Depth Duration Analysis ○ Frequency-based estimates of D-Day rainfall ○ Design precipitation depths for various return periods are determined Probable maximum precipitation ○ The greatest depth of precipitation for a given duration is physically possible in an area ○ Storm transposition is used in watersheds that have inadequate rainfall data or have experienced no severe storms ○ Transposition of storms from one watershed to another is based on the assumption that these storms could occur in the watershed under consideration ○ Storms occurred in the watershed under consideration and nearby watersheds which are meteorologically homogeneous adjacent catchments  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 31 Steps ○ Assurance of meteorological homogeneity ○ Selection and analysis of major recorded floods 4. Areal precipitation by an Isohyetal map specifying the spatial pattern of the precipitation Frequency analysis of areal precipitation is not commonly used Point precipitation estimates are extended to develop an average precipitation depth over an area Depth area duration (DAD) analysis ○ Distribution of rainfall amounts for various areas ○ Depth area relationships for various durations are derived by depth area duration analysis Isohyetal maps are derived for each duration MAX-DEPTH DURATION CURVE is a graph that depicts the relationship between water depth (typically resulting from precipitation or runoff) and the duration for which that depth is equaled or surpassed at a particular site or within a watershed. This curve is especially valuable in hydrology and water resource management as it helps in comprehending the fluctuations in water levels over time. Intensity Duration Frequency (IDF) Relationship - explains how rainfall intensity changes in relation to the duration of a rain event and the likelihood of specific  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 32 intensities occurring. This relationship is crucial for designing systems for managing stormwater, drainage infrastructure, and flood control strategies. DESIGN RUNOFF - describes the expected water flow over a surface during rainfall or storm events. It plays an essential role in civil engineering and urban planning for creating effective drainage systems, stormwater control, and flood prevention measures. The calculation of design runoff considers various factors, such as the size of the area, the rainfall’s intensity and duration, land use, and the type of soil. These factors help determine the volume and rate of runoff that needs to be managed to avoid flooding and soil erosion. 4.5 Design Precipitation Hyetographs Design Precipitation Hyetographs are graphical representations that depict the variation of rainfall intensity over time during a specific storm event. These hyetographs are crucial in hydrological engineering to estimate the temporal distribution of precipitation and the subsequent runoff, which aids in the design of stormwater infrastructure such as drainage systems, retention basins, and flood control measures. The hyetograph helps engineers and planners determine how much water falls over a watershed during a storm and how that water interacts with the landscape.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 33 A hyetograph is a graphical representation of rainfall intensity over time during a specific storm event. It shows how rainfall is distributed during a storm, allowing hydrologists and engineers to analyze and predict the amount of runoff and flooding that could occur as a result. A precipitation hyetograph typically consists of: Time (X-axis): This axis represents the duration of the storm event, usually divided into small time intervals (e.g., minutes or hours). Rainfall Intensity (Y-axis): This axis represents the rate of rainfall, typically measured in millimeters per hour (mm/h) or inches per hour (in/h). Cumulative Rainfall: Some hyetographs also show the cumulative rainfall over the duration of the storm, which represents the total volume of precipitation.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 34 Metrics employed for evaluating five types of hydroclimatic extremes: (a) Precipitation hyetograph (including infiltration loss curve indicating excess rainfall); (b) Flood hydrograph; (c) Drought; (d) Temperature; (e) Wind (storms). All these variables can be described using indicators of event duration and magnitude (peak intensity). 4.6 Design Runoff RUNOFF The flow of water across the earth. Surface runoff or overland flow that flows over land before reaching a watercourse. Streamflow, channel runoff, or river runoff once in a watercourse. The portion of precipitation that appears in surface streams. It can come from both natural processes and human activity.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 35 SEWER STORM DESIGN One of the most important facilities in preserving and improving the urban water drainage system. Construction of houses, commercial buildings, parking lots, paved roads, and streets increases the impervious cover in the watershed and reduces infiltration. Also, with urbanization, the spatial pattern of flow in the watershed is altered and there is an increase in the hydraulic efficiency of flow through artificial channels, curbing, gutters, and storm drainage and collection systems. One view of the typical urban drainage system is shown in the figure above. The system can be considered as consisting of two major types of elements: location elements and transfer elements. PIPE CAPACITY FOR STORM SEWERS Assumption: pipe is flowing full under gravity MANNING’S EQUATION  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 36 Note: Valid for Q in cfs and D in ft. For SI units (Q in m3/s and D in m), replace 2.16 with 3.21 and 1.49 to 1.0 WHERE: Q = flow rate n = manning’s roughness coefficient A = Cross sectional Area flow or flow area R = hydraulic radius S = slope of the channel D = diameter of pipe The Rational Method will also be used for the computation of the pipe capacity for storm sewers whereas it limitations and assumptions are as follows: The drainage area should not be larger than 200 acres. The peak flow is assumed to occur when the entire watershed is contributing runoff. The rainfall intensity is assumed to be uniform over a time duration equal to or greater than the time of concentration, Tc.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 37 The peak flow recurrence interval is assumed to be equal to the rainfall intensity recurrence interval. In other words, the 10-year rainfall intensity is assumed to produce the 10-year flood. RUNOFF COEFFICIENT The Runoff coefficient C is the least precise variable of the rational method. Its use in the formula implies a fixed ratio of peak runoff rate to rainfall rate of the drainage basin, which in reality is not the case. Proper selection of the runoff coefficient requires judgment and experience on the part of the hydrologist. RAINFALL INTENSITY The rainfall intensity I is the average rainfall rate in inches per hour for a particular drainage basin or subbasin. The intensity is selected on the basis of the design rainfall duration and return period. The design duration is equal to the time of concentration for the drainage area under consideration.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 38 Additional DRAINAGE AREA The size and shape of the catchment or sub catchment under consideration must be determined. The area may be determined by plan metering topographic maps, or by field surveys where topographic data has changed or where the mapped contour interval is too great to distinguish the direction flow. Sample Problem Given Td =10 min, C = 0.6, ground elevations at the pipe ends (498.43 and 495.55 ft), length = 450 ft, Manning n = 0.015, i=120T0.175/ (Td + 27), compute flow, pipe diameter and flow time in the pipe.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 39 solution:  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 40 4.7 Flood Control Reservoir Design and Modified Rational Method FLOOD CONTROL RESERVOIR is a large artificial or natural body of water designed to temporarily store excess rainwater or runoff during heavy rainfall events, thereby reducing the risk of flooding downstream. These reservoirs play a crucial role in managing water flow and protecting communities and infrastructure from flood damage. FLOOD CONTROL RESERVOIR DESIGN refers to the planning and construction of reservoirs that are specifically engineered to manage and mitigate the impact of floods. These reservoirs temporarily store excess runoff during heavy rainfall or snowmelt events and gradually release the water at controlled rates to reduce the risk of downstream flooding. Key aspects of flood control reservoir design include: 1. Storage Capacity: The reservoir must be large enough to accommodate peak floodwaters and prevent overflow. 2. Dam or Barrier Construction: A dam or similar structure is often used to create a reservoir to safely hold back large volumes of water during a flood event. 3. Inflow and Outflow Management: Inlet and outlet structures are designed to regulate the flow of water into and out of the reservoir, ensuring that it fills and drains at appropriate rates to reduce downstream impact.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 41 4. Spillways: Spillways are incorporated into the design to safely direct excess water when the reservoir reaches its capacity, preventing uncontrolled flooding or dam failure. 5. Flood Routing: This involves modeling the expected inflows and outflows during flood events to ensure that the reservoir can mitigate floods effectively without causing damage upstream or downstream. 6. Sediment Control: The design must also account for sediment carried by floodwaters, which can reduce the reservoir’s capacity over time. 7. Environmental and Social Considerations: The design often takes into account the potential ecological and social impacts, including habitat disruption, water quality, and effects on surrounding communities. MODIFIED RATIONAL METHOD The Modified Rational Method uses the peak flow calculating capability of the Rational Method paired with assumptions about the inflow and outflow hydrographs to compute an approximation of storage volumes for simple detention calculations. The rising and falling limbs of the inflow hydrograph have a duration equal to the time of concentration (tc). An allowable target outflow is set (Qa) based on pre-development conditions. The storm duration is td, and is varied until the storage volume (shaded gray area) is maximized. Moreover, This method was developed so that the concepts of the rational method could be used to develop hydrographs for storage design, rather than  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 42 just flood peak discharges for storm sewer design. The modified rational method can be used for the preliminary design of detention storage for watersheds of up to 20 or 30 acres. ILLUSTRATION OF MODIFIED RUNOFF  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 43 Sample Problem. Figure 2.  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 44 It is a series of “Trapezoidal” shaped hydrographs created for different Storm Durations. The “I” in the Rational equation is based upon the duration and not the Time of Concentration, However the hydrographs initially peak at the original Time of Concentration. The runoff volume from the pre-development hydrograph is subtracted from each of the runoff volumes (areas under the Trapezoid), for each storm duration. The greatest difference in volume between the pre and post hydrographs becomes your critical hydrograph with respective critical storm duration. Construct a series of hydrographs for each selected duration of the storm as shown in figure 2, Modified Rational Method Hydrographs. The estimated critical storage for this site is 88,858 cubic feet. Since the inflow volume must equal the outflow volume of 98,794 cubic feet, the time to the end of the release rate is 30.3. To reach zero outflow approximately 0.5 hours must be added so the total dewatering time will be about 30.3 hours. The outflow hydrograph reaches maximum flow at the intersection with the falling limb of the hydrograph resulting from a storm with a duration equal to the time of concentration. GIVEN: Runoff Coefficient (C) = 0.7 Area (A) = 11.88 acres  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 45 SOLUTION For Column 3 Peak Flow = Q = C i A = 0.7 * 4.8 * 11.88 = 39.9 cfs  Republic of the Philippines NUEVA ECIJA UNIVERSITY OF SCIENCE AND Cabanatuan City, Nueva Ecija, Philippines 46 For Column 4 Runoff Volume = Q * Duration of Storm * 3600 sec = 39.9cfs * 0.25hrs * 3600 sec = 35,925 cu.ft For Column 5 Release Volume = 0.92cfs * Duration of Storm * 3600sec = 0.92 cfs * 0.25hrs * 3600sec = 828 cu.ft For Column 6 Required Storage = Runoff Volume – Release Volume = 35,925 – 828 = 35,097 cu.ft