The design of a culvert or sewer for gravity flow involves three basic steps:

        Determine required flow
        Select pipe size
        Calculate flow velocity 

    The required flow is the maximum flow rate expected through a pipe during its design life. Required flow is determined by codes or local hydrology practice.

    The pipe size is selected using Manning's equation:
                    
                           
     where:
            Q = Flow rate, cubic feet per second
            A = Cross-sectional area of flow, square feet
            n = Roughness coefficient
            R = Hydraulic radius of flow, feet
            S = Slope of pipe, feet per foot

    The cross-section area, hydraulic radius and roughness coefficient are functions of the pipe shape and material. The slope is generally controlled by the site conditions.

    Velocity of flow within the pipe is found by the equation:
            Q = VA
    where:
            Q = Flow rate, cubic feet per second
            V = Velocity of flow, feet per second
            A = Cross-sectional area of flow, square feet

    Minimum and maximum flow velocity should be checked for proper performance of the pipe. Minimum velocities in sewers must be maintained for self-cleaning and the prevention of hydrogen sulfide buildup. High velocities in culverts may cause stream bed erosion at the outlet.

    The performance of sewers and long culverts is dependent on the roughness coefficient, n. The following paragraphs describe the importance of roughness coefficients in hydraulic design.

   ROUGHNESS COEFFICIENT
   Manning's roughness coefficient, n, is a function of the pipe material. Pipe material may be classified as smooth, such as concrete, cast iron, and some plastics, or rough, such as corrugated metal and other plastics. The n values for concrete pipe were established as 0.009 to 0.011 in studies performed at the St. Anthony Falls Hydraulic Laboratory. These values were recently confirmed by the Utah State University Foundation. Roughness coefficients for other smooth pipe material have been found to be similar. For corrugated metal pipe, the Federal Highway Administration (FHWA) recommends n values of 0.024 to 0.033, depending on the corrugation pattern.

    All roughness coefficients were determined under laboratory conditions using straight pipelines and clean water. However, connections, bends, manholes, grease and slime buildup, and other factors must be considered during design. Some smooth pipe material manufacturers claim that test values of n = 0.009 can be used for design purposes, but experienced engineers use n = 0.012 for storm sewers and culverts and n = 0.013 for sanitary sewers to account for actual conditions.

    For lined corrugated metal pipe, low laboratory n values have been recommended. These n values should not be used for design because of the comparatively short life of the lining. As a minimum, the designer should use the FHWA recommended n values for corrugated metal pipe.

    Selection of the proper roughness coefficient is very important. If the selection is too low, the conduit will be undersized and will prematurely reach its capacity, resulting in possible property damage. If the selection is too high, the conduit will be over sized and become inefficient, expensive and may require excessive maintenance.

    COMPARATIVE ANALYSIS
    A comparison of pipe size and shape between smooth and rough pipe material may be made with Manning's equation. The equation can be simplified by using a pipe flow constant, C, based on the pipe size and roughness
             
where:
           
    The required flow constant C, for a particular flow rate is:
             
    If the flow constant of a pipe equals or exceeds the required flow constant, the design is satisfied.

EXAMPLE: Comparative Analysis. Compare the size and shape of smooth and corrugated pipe required to carry a storm water flow rate of 100 cubic feet per second in a long conduit installed on a one percent grade.
    
    The required flow constant is found by solving Equation 4: 
        
    The Hydraulic Properties charts, Figures 10 and 11, provide the C values for concrete pipe and corrugated metal pipe.

    The smallest circular concrete pipe with a C value that exceeds 1000 is 42 inches in diameter. By comparison, the smallest circular corrugated metal pipe is 54 inches in diameter. The following table summarizes possible solutions.