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 Austin
 Drainage Criteria Manual
 Section 3. STREET FLOW
 Appendix 3.3.0. DESIGN METHOD

  § 3.3.3. Parabolic Crowns

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  • Flows in the gutter of a parabolically crowned pavement are calculated from a variation of Manning's Equation, which assumes steady flow in a prismatic open channel. However, this equation is complicated and difficult to solve for each design case.

    To provide a means of determining the flow in the gutter, generalized gutter flow equations for combinations of parabolic crown heights, curb splits and street grades of different street widths have been prepared. All of these equations have a logarithmic form.

    Note: The street width used in this section is measured from face-of-curb to face-of-curb.

    A.

    Streets Without Curb Split. Curb split is the vertical difference in elevation between curbs at a given street cross section. The gutter flow equation for parabolic crown streets without any curb split is:

    log Q = K o + K 1 log S o + K 2 log y o (Eq. 3-3)

    Where,

    Q = Gutter flow, cfs

    S o = Street grade, ft/ft

    Y o = Water depth in the gutter, feet

    K o , K 1 , K 2 = Constant coefficients shown in Table 3-2 for different street widths:

    Table 3-2
    Coefficients for Equation 3-3, Streets Without Curb Split
    Street Width* (ft) Coefficients
    K o K 1 K 2
    30 2.85 0.50 3.03
    36 2.89 0.50 2.99
    40 2.85 0.50 2.89
    44 2.84 0.50 2.83
    48 2.83 0.50 2.78
    60 2.85 0.50 2.74
    *Note: Based on the Transportation Criteria Manual, the street width is measured from face-of-curb to face-of-curb (FOC-FOC).
    Source: City of Austin, Watershed Engineering Division

     

    B.

    Streets With Curb Split - Higher Gutter. The gutter flow equation for calculating the higher gutter flows is as follows:

    log Q = K 0 + K 1 log S 0 + K 2 log y o + K 3 (CS) (Eq. 3-4)

    Where,

    Q = Gutter flow, cfs

    S 0 = Street grade, ft/ft

    Y 0 = Water depth in the gutter, feet

    CS = Curb split, feet

    K o , K 1 , K 2 , K 3 = Constant coefficients shown in Table 3-3 for different street widths:

    Table 3-3
    Coefficients for Equation 3-4, Streets With Curb Split - Higher Gutter
    Street Width (ft) Coefficients Curb Split Range (ft)
    K 0 K 1 K 2 K 3
    30 2.85 0.50 3.03 -0.131 0.0-0.6
    36 2.89 0.50 2.99 -0.140 0.0-0.8
    40 2.85 0.50 2.89 -0.084 0.0-0.8
    44 2.84 0.50 2.83 -0.091 0.0-0.9
    48 2.83 0.50 2.78 -0.095 0.0-1.0
    60 2.85 0.50 2.74 -0.043 0.0-1.2
    Source: City of Austin, Watershed Engineering Division

     

    C.

    Streets with Curb Split - Lower Gutter.

    The gutter flow equation for the lower gutter is:

    log Q = K 0 + K 1 log S 0 + K 2 log y 0 + K 3 (CS) (Eq. 3-5)

    Where,

    Q = Gutter flow, cfs

    S 0 = Street grade in ft/ft

    Y 0 = Water depth in the gutter in feet

    CS = Curb split in feet

    K 0 , K 1 , K 2 , K 3 = Constant coefficients shown in Table 3-4 for different street widths:

    Table 3-4
    Coefficients for Equation 3-5, Streets With Curb Split - Lower Gutter
    Street Width (ft) Coefficients Curb Split Range (ft)
    K 0 K 1 K 2 K 3
    30 2.70 0.50 2.74 -0.215 0.0-0.6
    36 2.74 0.50 2.73 -0.214 0.0-0.8
    40 2.75 0.50 2.73 -0.198 0.0-0.8
    44 2.76 0.50 2.73 -0.186 0.0-0.9
    48 2.77 0.50 2.72 -0.175 0.0-1.0
    60 2.80 0.50 2.71 -0.159 0.0-1.2
    Source: City of Austin, Watershed Engineering Division

     

    D.

    Parabolic Crown Location.

    The gutter flow equation presented for parabolic crowns with split curb heights is based on a procedure for locating the street crown. The procedure allows the street crown to shift from the street center line toward the high ¼ point of the street in direct proportion to the amount of curb split. The maximum curb split occurs with the crown at the ¼ point of the street. The maximum allowable curb split for a street with parabolic crowns is 0.02 feet per foot of street width.

    Example: Determination of Crown Location

    Given: 0.4 feet Design split on 30-foot wide street.

    Maximum curb split = 0.02 × street width
    = 0.02 × 30 feet = 0.6 feet

    Maximum Movement = ¼ street width for 30 foot street
    = ¼ × 30 feet = 7.5 feet

    Split Movement =(Design split × W/Maximum Split × 4)
    = (0.4 x 30/.6 × 4) = 5 feet

    Curb splits that are determined by field survey, whether built intentionally or not, should be considered when determining the capacity of the curb flow.

    Special consideration should be given when working with cross sections which have the pavement crown above the top of curb. When the crown exceeds the height of the curb the maximum depth of water is equal to the height of the curb, not the crown height. It should be noted that a parabolic section where the crown equals the top of curb will carry more water than a section which has the crown one (1) inch above the top of curb.