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The design equations used to develop the inlet control nomographs are based on the research conducted by the National Bureau of Standards (NBS) under the sponsorship of the Bureau of Public Roads (now the Federal Highway Administration). Seven progress reports were produced as a result of this research. Of these, the first and fourth through seventh reports dealt with the hydraulics of pipe and box culvert entrances, with and without tapered inlets (4,7 to 10) These reports were one source of the equation coefficients and exponents, along with other references and unpublished FHWA notes on the development of the nomographs. (56,57)

The two basic conditions of the inlet control depend upon whether the inlet end of the culvert is or is not submerged by the upstream headwater. If the inlet is not submerged, the inlet performs as a weir. If the inlet is submerged, the inlet performs as an orifice. Equations are available for each of the above conditions.

Between the unsubmerged and the submerged conditions there is a transition zone for which the NBS research provided by drawing a curve between and tangent to the curves defined by the unsubmerged and submerged equations. In most cases, the transition zone is the short and the curve is easily constructed.

Below are the unsubmerged and submerged inlet control design equations. Note that there are two forms of the unsubmerged equation. Form (1) is based on the specific head at critical depth, adjusted with two correction factors, Form (2) is an exponential equation similar to a weir equation. Form (1) is preferable from a theoretical standpoint, but form (2) is easier to apply and is the only documented form of equation for some of the inlet control nomographs. Either form of unsubmerged inlet control equation will produce adequate results.

Inlet Control Design Equations



HWi = Headwater depth above inlet control section invert, metres or feet

D = Interior height of culvert barrel, metres or feet

Hc = Specific height of culvert barrel, metres or feet

Q = Discharge, m3/s or ft3/s

A = Full cross sectional area of culvert barrel, metres2 or feet2

S = Culvert barrel slope m/m or ft/ft

K, M, c, Y = Constants from the table

  1. Equations for unsubmerged apply up to about Q/AD0.5 = 3.5
  2. For mitered inlets use + 0.75 instead of – 0.55 as the slope correction factor
  3. Equation for submerged applies above about Q/AD0.5 = 4.0

Constants for inlet control design equations

Inlet TypeDescriptionIndex Value
Circular ConcreteSquare edge with headwall        1
Groove end with headwall        2
Groove end projecting        3
Circular Corrugated Metal PipeHeadwall        4
Mitered to slope        5
Circular Pipe, Beveled Ring Entrance45 deg. bevels        7
33.7 deg. bevels        8
Rectangular Box; Flared Wingwalls 30-75 deg. wingwall flares        9
90 or 15 deg. wingwall flares        10
0 deg. wingwall flares (straight sides)        11
Rectangular Box; Flared Wingwalls and Top Edge Bevel45 deg flare; 0.43D top edge bevel        12
18-33.7 deg. flare; 0.083D top edge bevel        13
Rectangular Box, 90-deg Headwall, Chamfered / Beveled Inlet Edges  Chamfered 3/4-in.        14
Beveled 1/2-in/ft at 45 deg. (1:1)        15
Beveled 1-in/ft at 33.7 deg. (1:1.5)        16
Rectangular Box, Skewed Headwall, Chamfered / Beveled Inlet Edges  3/4" chamfered edge, 45 deg. skewed headwall        17
3/4" chamfered edge, 30 deg. skewed headwall        18
3/4" chamfered edge, 15 deg. skewed headwall        19
45 deg. beveled edge, 10-45 deg. skewed headwall        20
Rectangular Box, Non-offset Flared Wingwalls, 3/4" Chamfer at Top of Inlet  45 deg. (1:1) wingwall flare        21
18.4 deg. (3:1) wingwall flare        22
18.4 deg. (3:1) wingwall flare, 30 deg. inlet skew        23
Rectangular Box, Offset Flared Wingwalls, Beveled Edge at Inlet Top 45 deg. (1:1) flare, 0.042D top edge bevel        24
33.7 deg. (1.5:1) flare, 0.083D top edge bevel        25
18.4 deg. (3:1) flare, 0.083D top edge bevel        26
Corrugated Metal Box90 deg. headwall        27
Thick wall projecting        28
Thin wall projecting        29
Horizontal Ellipse ConcreteSquare edge with headwall        30
Grooved end with headwall        31
Grooved end projecting        32
Vertical Ellipse ConcreteSquare edge with headwall        33
Grooved end with headwall        34
Grooved end projecting        35
Pipe Arch, 18" Corner Radius, Corrugated Metal90 deg. headwall        36
Mitered to slope        37
Projecting (FHWA 1974)        38
Pipe Arch, 18" Corner Radius, Corrugated Metal  Projecting (Bossy 1963)39
No bevels        40
33.7 deg. bevels        41
Pipe Arch, 31" Corner Radius,Corrugated MetalProjecting        42
No bevels43
33.7 deg. bevels44
Arch, Corrugated Metal90 deg. headwall45
Mitered to slope46
Thin wall projecting47
Circular CulvertSmooth tapered inlet throat48
Rough tapered inlet throat49
Elliptical Inlet FaceTapered inlet, beveled edges50
Tapered inlet, square edges51
Tapered inlet, thin edge projecting52
RectangularTapered inlet throat53
Rectangular ConcreteSide tapered, less favorable edges54
Side tapered, more favorable edges55
Slope tapered, less favorable edges56
Slope tapered, more favorable edges57