American Concrete Pipe Association Professional Pipe Promotion A Technical and Sales/Marketing Training Program

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1 ACPA Technical Series Module I: Basic RCP Course 7: Basic Hydraulics Author: Tom Finn, ACPA Regional Engineer American Concrete Pipe Association Professional Pipe Promotion A Technical and Sales/Marketing Training Program Required Reading Concrete Pipe Design Manual, Chapter Hydraulics of Sewers Concrete Pipe Design Manual, Chapter 3 Hydraulics of Culverts Concrete Pipe Handbook, Chapter 3 - Hydraulic Design Concrete Pipe Handbook, Chapter 7 Design for Sulfide Control ACPA Brochure: Hydraulic Efficiency, Resource #07-17 ACPA Brochure: Underground Storm Water Storage Systems The Cost Effective, Efficient Way, Resource # Design Data 10 - Manning s n Values History of Research Design Data 11 Hydraulic Capacity of Culverts Design Data 1 Hydraulic Capacity of Concrete Boxes Design Data 16 Partial Flow Conditions for Culverts Design Data 17 Partial Flow Conditions of Box Culverts Design Data 18 Equivalent Flow Capacity of Various Pipe Materials You Should Know No. 133 Abrasion Affects Durability in Some Drainage Pipe Buried Facts: Hydraulic Design Considerations CP Info - Culvert Velocity Reduction by Internal Energy Dissipaters CP Info Culvert Velocity Reduction with an Outlet Expansion Additional Resources Federal Highway Administration Hydraulics Engineering website: Overview This course covers basic hydraulic concepts to provide a brief introduction of hydraulic concepts that are frequently used when designing projects that have a pipe system. Completion of this course should give the student a good understanding of basic hydraulics as well as common terms and their meanings as used in sewer and culvert applications. The ACPA has extensive hydraulic design information available through its website, if you would like a more in-depth explanation and examples of hydraulic analysis procedures. For most hydraulic calculations for pipe size for sanitary sewers, storm sewers and culverts, the design engineer can solve the problems by using a solely mathematical means or can use a graphical solution of Manning s formula to help solve the problem. In all but a few cases, the applications for reinforced concrete pipe will consist of systems that are under gravity flow and the fluids contained in the pipe system will be under no pressure. There are cases where a pipe might flow full and the pipe inlet is submerged, which can result in the pipe being slightly pressurized due to the force of water upstream pushing the water downstream. The discharge of a pipe or culvert is the quantity of water moving past a given plane (cross section) in a given unit of time (i.e. cubic feet per second). The plane or cross section should be perpendicular to the velocity vector. 010 American Concrete Pipe Association, all rights reserved 1

2 Since liquids are relatively incompressible, they are generally treated as wholly incompressible fluids; this includes water - it takes a great deal of pressure to accomplish a little compression. There are three basic equations of flow used for pipe and culvert analysis: continuity, energy and momentum. These basic formulas are derived from the laws of conservation of mass, the conservation of energy and the conservation of linear momentum. The conservation of mass is basically saying that matter can neither be created nor destroyed (ignoring mass-energy interchange). The principal of conservation of energy is based on the first law of thermodynamics, which is that energy must at all times be conserved. The principal of conservation of linear momentum is based on Newton s Second Law of motion, which states that a mass accelerates in the direction of and proportional to the applied forces on the mass. Hydraulics Basic Equations One of the basic formulas used in hydraulic analysis is the Continuity Equation, which applies to steady, compressible or incompressible flow within fixed boundaries. Simply stated if the flow is constant in a reach of a channel the product of the area and velocity will be the same for any two cross sections within that reach. The equation assumes that there is no significant inflow or leakage (or they area accounted for) in the system being analyzed. Q = A = V A V 1 1 Where: Q = the volumetric flow rate (cfs) A = the cross sectional area of flow (ft ) V = the average velocity in the cross section (ft/s) The energy equation is derived from the first law of thermodynamics which states that energy must be conserved at all times. p 1 z 1 V1 g = p z V g h L Where, V = Average velocity in the cross section (ft/s) g = Acceleration of gravity, (3. ft/s ) P = Pressure, psi γ = Unit weight of water, force per unit volume (lbf/ft 3 ) h L = Headloss (ft) The momentum equation is derived from Newton s Second Law that states the sum of all external forces on a system is equal to the change in momentum. The equation below is for steady flow, with a constant density and in the x-direction. Where, = Q V ) F X ( V American Concrete Pipe Association, all rights reserved

3 F x = Forces in the x direction β = Momentum coefficient Q = Volume flow rate or discharge V = Velocity in the x direction ρ = Density The momentum coefficient acts to correct for the velocity distribution across the flow. It is normally assumed to be 1.0 because a very uniform velocity distribution across a section would only require a correction less than 10 percent. Since the momentum equation is a vector equation, similar equations are used for the y and z direction. Open Channel Flow Open channel flow is where the fluid passage way allows part of the fluid to be exposed to the atmosphere and thus flows under gravity flow. Natural Waterways Canals Flumes Culverts Pipes flowing under the influence of gravity (pressure conduits always flow full) Difficulties in calculating flows under open channel flow: Variations in cross sections and roughness More empirical & less exact than pressure conduit flow Run-off calculations used to calculate stormwater flow imprecise Flow can be classified as: 1. uniform or nonuniform;. steady or unsteady flow; 3. laminar or turbulent flow; and 4. subcritical (tranquil) or supercritical (rapid) flow In uniform flow, the depth, discharge, and velocity remain constant with respect to distance. In steady flow, no change occurs with respect to time at a given point. Laminar flow (also known as streamline flow) is where the fluid appears to move by the sliding of laminations of infinitesimal thickness relative to adjacent layers. The particles move in definite and observable paths or streamlines. Turbulent flow is represented by the irregular motion of a large numbers of particles during a brief time interval. A distinguishing characteristic of turbulence is in its irregularity, having no definite frequency, as in wave action, and has no observable pattern, as in the case of large eddies. Turbulent flow is characterized by fluctuations in velocity at all points of the flow field. The flow is influenced by eddies which interact with each other and the general flow which acts to dissipate their energy. Open Channel flow is almost always turbulent; laminar flow will occur only in very shallow channels or at low fluid velocities. Open channel-channel flow s response to changes in channel geometry depends upon the depth and velocity of the flow. 010 American Concrete Pipe Association, all rights reserved 3

4 Subcritical flow (or tranquil flow) occurs on mild slopes where the flow is deep with a low velocity. In subcritical flow, the boundary condition (control section) is always at the downstream end of the flow reach. Supercritical flow occurs on steep slopes where the flow is shallow with a high velocity. In supercritical flow, the boundary condition (control section) is always at the upstream end of the flow reach. Pressure Flow Pressure flow implies that the flow occurs under pressure. Gases always flow under pressure flow conditions. When a liquid flows with a free surface (for example, a partially full pipe) the flow is referred to as gravity flow because gravity is the primary force moving the liquid. The flow quantity (Q) is found by multiplying the mean velocity (v) by the flow area (A). Q = va Manning s Formula One of the best and most widely used formulas for calculating open-channel flow is the Manning s formula which was first published in 1890 by Robert Manning. The Manning Formula continues to be popular because it is simple to use and provide reasonably accurate results. Manning s Formula: Q = va = n AR 3 S 1 Where, Q = Flow Quantity/Volume, the quantity of fluid flowing per unit time across any section (cubic feet per second CFS) A = Cross-sectional Area of Flow (ft ) v = velocity (mean velocity) (i.e. feet per second ft/s) R = Hydraulic Radius (ft) P = Wetted Perimeter (ft) S = Slope (ft/ft) n = Manning Roughness Coefficient The hydraulic radius is the ratio of the area in flow to the wetted perimeter (R=A/P). For a circular channel flowing either full or half full, the hydraulic radius is one-forth of the equivalent diameter. The Manning s n is a coefficient which represents the roughness or friction applied to the flow by the channel. Although all smooth wall pipes, such as concrete and plastic, were found to have n values ranging between and 0.010, these values are from laboratory tests. Design engineers familiar with sewer design use a n value between 0.01 and The difference in the values takes in account the difference between laboratory testing and actual installed conditions. It should be noted that corrugated plastic pipe does not truly have a smooth interior surface, and after time corrugated HDPE pipe will experience corrugation growth that occurs along the interior pipe. When corrugation growth occurs, it acts to create waviness in the interior pipe wall and will make the interior of the HDPE pipe similar to corrugated metal pipe. For this 010 American Concrete Pipe Association, all rights reserved 4

5 reason it is recommend that that a Manning s n value similar to corrugated metal pipe be used for corrugated HDPE pipe design. After the design flows have been calculated for the pipe system, the pipes size is then selected using Manning s Formula. The formula can be solved by selecting a pipe roughness coefficient with either a known or assumed slope and then working backwards to find the size of pipe needed to carry the flow. More than likely the pipe size will be between two standard pipe sizes and the designer should select the larger of the pipes for the system. Basic Hydraulic Concepts of Sanitary Sewers Sanitary sewers are designed to carry domestic, commercial and industrial sewage and in most cases added capacity is designed for to include infiltration of groundwater into the system. In designing sanitary sewers the designer considers average, peak and minimum flows. All the types of flow are designed on the basis of having the flow characteristics of wastewater. The flows used for design can be derived from past data or can be calculated using set variables that take into consideration the population and use of areas (domestic, commercial) that will be served by the sanitary sewer. Average Flow Average flow is usually expressed in gallon per day (gpd) of flow. The average flow is a hypothetical quantity. The average rate of water consumed by the household or commercial property is sometimes related to what the contribution or average flow of wastewater that would be received by the system. To apply flow criteria to the design of a sanitary sewer system present and future population densities as well as the types of business and industry contained in the area to be served by the sanitary sewer need to be determined. Peak Flow The actual flow in a sanitary sewer system is variable depending on the season, day and hour. It s the peak flow when considering all variables, that the sanitary sewer must be designed to carry. The peak flow is defined as the maximum flow for a 15 minute period for any 1-month period and is determined by multiplying average daily flow by an appropriate factor. The factor is sometime given by the municipality where the sanitary sewer will be in service. Minimum velocity requirements are in place for most municipalities and it is usually given as.0 feet per second when flowing full or half full. This minimum velocity is an effort to keep the velocity of the fluid in the pipe above the point where suspended solids will begin to settle out at the bottom of the pipe. Manning s n Value It is recommended that a Manning s n value of is used for sanitary sewers. By using the Manning s formula, a designer can use graphical solutions to determine the resulting pipe size and velocity when the flow, slope and roughness coefficient are known. The designer can also use the Manning s formula to calculate all the required variables to design a pipe that would carry the design flow. Basic Hydraulic Concepts of Storm Sewers Storm sewers are designed to carry precipitation runoff, surface waters and in some cases groundwater flow. The hydraulic sizing of drainage and conveyance structures in urban settings always requires estimation of peak flows. 010 American Concrete Pipe Association, all rights reserved 5

6 Determining Design Flow For reservoir and dam design, the total runoff volume is required. However, to size storm sewers and culverts the instantaneous peak runoff is needed. The Rational Method has been widely by design engineers since the early 1900s to determine design flows in urban and small watersheds. The Rational Method is applicable to areas smaller to 1 to square miles. For larger areas it is recommended that the designer use a software program to calculate amount of runoff the system needs to be capable of carrying. The intensity variable depends on the time of concentration and the degree of protection desired (the recurrence interval or design storm). Q = CiA Where, Q = Flow (cfs) i = Rainfall intensity, duration equals time of concentration of the basin (in/hr) C = Runoff coefficient, dimensionless A = Drainage Area (ac) The runoff coefficient C is the ratio of the average rate of rainfall on an area to the maximum rate of runoff. The rainfall intensity i is the amount of rainfall measured inches per hour that would be expected to occur during a storm of certain duration. Time of concentration is composed of three components: sheet (overland) flow, concentrated flow (swales, natural channels), and the flow in lined canals or closed conduits. The time of concentration at any point in a sewer system is the time required for runoff from the most remote portion of the drainage area to reach that point. The runoff coefficient and the drainage area are both constant for a given area at a given time. Accurate values of C depend on not only on the surface cover and soil type, but also on the recurrence interval, antecedent moisture content, rainfall intensity, drainage area, slope and impervious cover. If more than one area contributes to the runoff, the coefficient is weighted by the areas. The rational method assumes that rainfall occurs at a constant rate and then the peak runoff will occur when the entire drainage area is contributing to surface runoff. The Rational Method also assumes that the recurrence interval of the peak flow is the same as for the design storm; the runoff coefficient is constant; and the rainfall is spatially uniform over the drainage area. Storm sewers are designed on the presumption that they will flow full during the design storm event. The design storm or storm frequency is either given by agency where the storm sewer will be located or can be selected through consideration of the size of the drainage area, probable flooding and land use consideration for the area to be addressed. Minimum velocity requirements higher than that of sanitary sewers. The debris in entering a storm water sewer will generally have a higher specific gravity that sanitary sewage. A minimum velocity of 3 feet per second is usually specified. Manning s n Value It is recommended that a Manning s n value of 0.01 be used for storm sewers. By using the Manning s formula, a designer can use graphical solutions to determine the resulting pipe size and velocity when the flow, slope and roughness coefficient are known. The designer can also use the Manning s formula to calculate all the required variables to design a pipe that would carry the design flow. 010 American Concrete Pipe Association, all rights reserved 6

7 Basic Hydraulic Concepts of Culverts The purpose of highway drainage is to prevent water standing on the surface of the highway and convey the off-site storm runoff from one side of the roadway to the other. Culverts are closed conduits in which the top of the structure does not form part of the roadway. Headwater is the depth of water at the upstream face of the culvert. The main reason for the accumulation of water is to build up the energy required to pass the water through the culvert opening and to overcome the friction, entrance, and exit along the culvert. The designer should not ignore the design limitations on the maximum or allowable headwater (AHW). AHW is the level to which the culvert headwater may rise before causing an unwanted inundation or damage under the circumstances of the design flood. When designing culverts, the designer should consider AHW design limitations: AHW should not cause damage to upstream properties AHW should be below the traffic lanes of interest or lower than the road shoulder AHW should be lower than the low point in the road grade AHW should not be equal to the elevation where the flow diverts around the culvert The tailwater is the depth of water downstream of the culvert measured from the outlet invert. The tailwater can be a significant factor in designing the culvert for proper hydraulic operation. The depth of the tailwater can affect the outlet velocity, and depending on the character of the culvert flow it can also affect the operating headwater on the culvert. For design purposes the outlet velocity should be similar in magnitude to the velocity in the channel to provide appropriate protection at the downstream end. The outlet velocity can be controlled by the size or the roughness of the culvert, stabilization of the channel or by constructing energy dissipation structures. The ideal minimum velocity should be adjusted such that the sediment particles suspended in the storm water transported through the culvert will not be allowed to settle. In case of unknown stream bed material, the designer should size the culvert to maintain a velocity of.5 feet per second within the culvert. Culvert Discharge A culvert can operate under either inlet or outlet control depending on if the culvert barrel or the inlet structure of the culvert has a greater hydraulic capacity. If the control section is located at or near the culvert entrance and the discharge is dependent only on the inlet geometry and headwater depth the culvert it said to have inlet control. In other words, a culvert will operate under inlet control when the culvert barrel has a higher hydraulic capacity than that of the inlet. Culverts operating under inlet control will always flow partially full. Inlet Control Characteristics Barrel hydraulic capacity is higher than that of the inlet. Typical flow condition is critical depth near the inlet and supercritical flow in the culvert barrel. Due to constriction at entrance, the inlet configuration has a significant effect on hydraulic performance. If the control section is located at or near the culvert outlet and the discharge is dependant on all of the hydraulic factors upstream from the outlet such as shape, slope, length, surface roughness, tailwater depth, headwater depth and inlet geometry, the culvert is said to have outlet control. In 010 American Concrete Pipe Association, all rights reserved 7

8 other words, a culvert will operate under outlet control conditions if the culvert barrel has a smaller hydraulic capacity than the inlet does. Outlet Control Characteristics Barrel hydraulic capacity has a smaller hydraulic than the inlet does. Typical flow condition is that the full or partially full culvert barrel for all or part of its length. Flow regime is always subcritical, so the control of flow is either at the downstream end of the culvert or further downstream of the culvert outlet. There is one depth, known as critical depth that minimizes the flow energy. Critical flow occurs when the sum of kinetic energy (velocity head) plus potential energy (depth head) for a given discharge is at a minimum. There are many hydraulic design procedures available for determining the proper culvert size, some of which can be an involved comprehensive mathematical analysis and an iterative process. The Concrete Pipe Design Manual gives a detailed method for calculating culvert size by use of culvert capacity charts. Below is an outline of AASHTO s Culvert Design Procedure that gives the steps that are required to design and size culverts. AASHTO Culvert Design Procedures: Establishment of Hydrology Design of downstream channel Assumption of a trial configuration Computation of inlet control headwater Computation of outlet control headwater at inlet Evaluation of the controlling headwater Computation of discharge over the roadway & total discharge Computation of outlet velocity and normal depth 010 American Concrete Pipe Association, all rights reserved 8