Hydraulic flow rates through culverts are dependent on the inlet geometry, slope, length, roughness coefficient, headwater depth, and tailwater elevation. These factors are used to determine the section of the culvert that controls flow. The two principal types of flow in a culvert are inlet control and outlet control. The control conditions are described in the following illustrations.

   Inlet control exists when the control section is located at or near the culvert entrance. Flow through the culvert is dependent on the size and shape of the inlet and on headwater depth. Since water can run out of the culvert faster then it can enter, the culvert will be partially full. Maximum flow occurs with inlet control.

    Outlet control exists when the control section is located at or near the end of the culvert. Flow through the culvert is dependent on the culvert's hydraulic characteristics and the field observed headwater and tailwater elevations. Water cannot run out of a culvert as fast as it can run in and may flow partially or completely full.

    The slope and pipe roughness are major factors in determining whether the flow in a culvert will be inlet control or outlet control. Smooth pipe maintains inlet control and greater flow capacity through a much larger range of slopes when compared to rough pipe. A rough pipe with comparable entrance conditions as a smooth pipe will require a much steeper slope to provide a comparable flow.

    Three basic steps are required to design a culvert:

        Determine required flow
        Select pipe size
        Calculate flow velocity

    DETERMINE REQUIRED FLOW: Flow through culverts is a result of storm water runoff. Runoff in small water sheds is usually determined by the Rational Method. The method directly relates runoff to the drainage area, the rainfall intensity, and the coefficient of runoff. Rainfall intensity is a function of storm frequency and duration. Typically, a storm frequency of 50 years is used for culvert design. The coefficient of runoff represents the ratio of runoff to rainfall and considers ground cover, soil type, and topography. The required flow used for design in a culvert is the maximum flow resulting from the collection of runoff at any point in the system. The Rational Method is described in more detail in the ACPA Concrete Pipe Design Manual. Local conditions can be obtained from the U.S. Weather Bureau, state transportation department's manuals and other sources.

    Inspection of existing nearby drainage structures should be made to verify assumptions used for the new culvert design. The required flow calculated by the Rational Method may be confirmed by noting the high water elevations and hydraulic characteristics of the existing structure.

    SELECT PIPE SIZE: The pipe size may be determined by either the Culvert Capacity charts, Figures 16 through 22, or the Culvert Nomographs, Figures 23 through 28. The Culvert Capacity charts have been developed from the inlet and outlet control nomographs. The nomographs were first published in the Bureau of Public Roads Hydraulic Engineering Circular No. 5, Hydraulic Charts for the Selection of Highway Culverts.

    The Culvert Capacity charts provide the flow rate through a culvert. Culvert diameters are represented by curves that are numerically labeled by the length/slope ratio L/100S_o, where L is the culvert length in feet and S_o is the culvert slope in feet per foot.

    The solid curve represents the maximum length/slope ratio for which inlet control exists. Any point on a solid curve gives the minimum headwater depth necessary to develop the required flow rate. Points above the solid line represent outlet control. The dashed curve is the upper limit of the accuracy of the charts. The horizontal dotted line denotes headwater depth approximately two times the vertical dimension of the culvert. Accuracy of the charts decrease as the headwater increases above the dotted line. Charts can only be used when the culvert outlet is not submerged.

    Large sized culverts are represented by only inlet control curves. Large culverts are rarely controlled at the outlet.

    To select pipe size from the Culvert Capacity charts, the required flow, length/slope ratio, and allowable headwater elevation must be known. The culvert length, slope and allowable headwater are determined from site conditions. For the required Q and the length/slope ratio, select the smallest diameter pipe on the appropriate chart that does not exceed the allowable headwater elevations.

    Inlet and outlet control nomographs may be used to determine culvert size for all hydraulic conditions but must be used where Culvert Capacity charts are limited in accuracy. Selecting pipe diameter with nomographs requires a complex trial and error method while the charts provide a direct solution.

    To use the nomographs, the culvert size must be first estimated. The culvert diameter or rise can be assumed to be approximately 50 percent of the allowable headwater depth. Using estimated culvert size, the headwater depth must be determined on the inlet control nomograph. If the inlet control headwater depth is less than the allowable headwater depth, the culvert must then be checked for outlet control using the outlet control nomograph. If the outlet control headwater is also less the allowable headwater, the culvert size is adequate. If the headwater depths exceed the allowable, a larger sized culvert must be tried. The type of control for the culvert is found by comparing the headwater depths from the inlet and outlet control nomographs. The greater headwater depth identifies the type of control.

    Culvert Capacity charts and Culvert Nomographs are not available for concrete arch pipe. Arch pipe size may be selected using charts and nomographs for horizontal elliptical pipe. To select the size of an arch pipe, increase the required flow by the factors listed in the following table.

Determine the equivalent circular pipe size from the horizontal elliptical pipe charts or nomographs. The comparable arch pipe size can be selected from the Hydraulic Properties for Arch Pipe chart, Figure 11.

    CALCULATE FLOW VELOCITY. Outlet velocity of a culvert is higher than the velocity of the natural stream bed because of improved hydraulic conditions. Excessive energy from the higher velocity may damage or erode the stream bed which could result in loss of foundation support for the culvert structure. The energy may be absorbed by tailwater if proper conditions exist, by stream bed protection, or dissipated with precast flared end sections and velocity reduction rings. Special consideration should be given to culverts with outlet velocities exceeding ten feet per second. The outlet velocity of inlet and outlet controlled culverts must each be calculated differently.

    For inlet controlled culverts, the actual velocity is proportional to the full flow velocity in the pipe. To determine this proportion, the Full Flow Curves, Figures 1 through 6, and the Relative Velocity and Flow curves, Figures 7 through 9, are used. The Full Flow Curves with n=0.012 are used first to find the full flow rate and velocity in the culvert. The ratio of required flow to full flow must then be calculated. This ratio is used in the Relative Velocity and Flow curves to find the proportion of actual velocity to full flow velocity. The actual velocity can then be calculated by multiplying the full flow velocity and the proportion from the Relative Velocity and Flow curves.

    For outlet controlled culverts, the actual velocity is equal to the flow rate divided by the flow cross-sectional area. When the outlet is submerged, there is full flow and the cross-sectional area of the pipe is used to solve for velocity. When the outlet is not submerged, there is partial flow at the outlet. The velocity is determined at a point in the culvert where the flow depth is equal to the critical depth, d_c, or tailwater depth, whichever is greater. Critical depth is found on the Critical Depth Charts, Figures 29 and 30.

    The flow at depth d_c is proportional to the area of the pipe. To find the ratio of partial flow area to full flow area, enter the Relative Velocity and Flow charts, Figures 7 through 9, with the proportion of critical depth to pipe diameter. The flow area curve on the charts multiplied by the pipe cross-sectional area. The flow velocity can then be calculated by dividing the flow rate by the flow area.

EXAMPLE: Culvert Size by Culvert Capacity Chart. Select the size of a circular concrete pipe for a site where the allowable headwater depth is seven feet and the tailwater depth is low. The culvert length is 200 feet with a slope of 0.01 feet per foot. the required flow rate has been determined to be 150 cubic feet per second.

   To use the Culvert Capacity charts, the length/slope ratio must be calculated. For this example the ratio is:
                    
The curves on Figure 16 provide culvert size selections for hydraulic flow rates of 0 to 350 cubic feet per second. On the lower set of curves where Q=150 cubic feet per second on the horizontal axis, project a line vertically to the smallest sized pipe below the allowable headwater depth of seven feet. The 54 inch inlet control curve labeled with a length/slope ratio of 600 intersects the 150 cubic feet per second line at a headwater depth of six feet. The actual length/slope ratio of 200 is below the inlet control curve, therefore flow is controlled at the inlet.

   The outlet velocity is found using the Full Flow Curves for Circular Pipe, n=0.012, Figure 2, and the Relative Velocity and Flow curves, Figure 7. From Figure 2, the full flow discharge for a 54 inch diameter circular pipe installed on a one percent slope is 215 cubic feet per second at a velocity of 13.5 feet per second. The proportion of required flow to full flow is:
           
               

   On Figure 7, for circular pipe, extend a vertical line from 0.70 on the horizontal axis to the discharge curve. Extend a horizontal line to the velocity curve. Project a line vertically to the proportional value of 1.07 on the horizontal axis. The partial flow velocity is:

           
EXAMPLE: Culvert Size by Culvert Nomographs. Select the size of a circular concrete pipe culvert for a site where the allowable headwater depth is five feet and the tailwater depth is low. The culvert length is 200 feet with a slope of 0.002 feet per foot. The required flow rate is 50 cubic feet per second.

   Use of the Culvert Nomographs is a trial and error procedure. The initial estimated trial diameter of the culvert is one-half of the allowable headwater depth, or 30 inches. On the Culvert Nomograph for Circular Concrete Pipe Culverts with Inlet Control, Figure 23, draw a straight line from the 30 inch size location on the diameter scale through the 50 cubic feet per second point on the discharge scale to the headwater/depth scale. The headwater/depth ratio if 1.92, therefore the headwater depth is:
       
    The 30 inch diameter culvert will work with inlet control Headwater depth for outlet control must be found next.

   The equation for headwater depth, HW, for outlet control is:

       
    where
        H  = Head on culvert, feet
        h_o = Outlet head, the greater value of either
                or tailwater depth
        D  = Culvert diameter, feet
        d_c = Critical depth, feet
        L  = Culvert length, feet
        S_o= Culvert slope, feet per foot

    The outlet control nomographs solve one component, H, of the equation used to find headwater depth.

   On the Culvert Nomograph for circular concrete Pipe culverts with Outlet Control, Figure 26, locate the 30 inch trial size culvert on the diameter scale. From that point draw a straight line to 200 feet on the culvert length scale. Locate the flow of 50 cubic feet per second on the discharge scale. From that point draw another straight line through the intersection of the first line and the turning line to the head scale. The head, H, is 4.6 feet.

   Because the tailwater is low, the outlet head, h_o, is:
       
   Critical depth, d_c, is estimated to be 2.3 feet by extrapolation on the Critical Depth Chart, Figure 29. The outlet head is:
       
   The outlet control headwater depth is:

       
                  
   The headwater exceeds the allowable headwater so the 30 inch diameter pipe is too small. A second trial must be made.

    For the second trial, a 36 inch diameter pipe is selected. The headwater depth is found using the same procedure as before. The outlet control headwater exceeds the inlet control headwater indicating the culvert has outlet control. The 36 inch diameter circular culvert has a 4.2 foot headwater depth and is adequate.

    Because this culvert has outlet control and low tailwater depth, the velocity is equal to the flow rate divided by the cross-sectional area of the flow where the depth is equal to the critical depth.

    The critical depth is found on the Critical Depth Chart, Figure 29. For a 36 inch diameter circular pipe and flow of 50 cubic feet per second the critical depth is 2.2 feet.

    To determine the area of flow at critical depth, the Relative Velocity and Flow curves, Figure 7, must be used. This chart requires the proportion of critical depth to pipe diameter. This ratio is:
       
    On Figure 7, locate the proportional value of 0.73 on the vertical axis. Project a horizontal line from this location to the water area curve. Extend a vertical line down to the horizontal axis at a proportional value of 0.81. This value is the proportion of flow area at the critical depth to the cross-sectional area. The area of flow at the critical depth is:

       
   The outlet velocity in the 36 inch culvert is:
         
       

EXAMPLE: Culvert Selection. This example illustrates that a variety of precast concrete products may be used as culverts at a particular site. The designer must then choose the culvert shape and size by considering other factors such as pipe and installation cost, weight, and site conditions.

    Determine the shape and required size of a culvert, and the outlet velocity if the discharge flow is 750 cubic feet per second. The allowable headwater depth is nine feet. The culvert length is 200 feet and the slope is 0.001 feet per foot. Culverts with large cross-sectional areas are usually inlet controlled.

    The Culvert Capacity charts, Figures 16 through 22, indicates that both a 12 foot span by 7 foot rise box section and a 108 inch equivalent size elliptical pipe are adequate. Single line circular pipe requires headwater depths greater than the allowable for the required discharge and cannot be used. Multiple lines of culverts can be used as an alternative to a single large culvert. Double lines of 84 inch circular pipe, 8 foot by 4 foot box sections or 84 inch equivalent size arch pipe are also adequate. The following table is a partial list of the precast concrete sections that meet the flow capacity requirements.