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(4,7 to 10) These reports were one source of the equation coefficients and exponents, along with other references and unpublished FHWA notes on the development of the nomographs.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

**Definitions:**

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

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

## Constants for inlet control design equations

Inlet Type | Description | Index Value |
---|---|---|

Circular Concrete | Square edge with headwall | 1 |

Groove end with headwall | 2 | |

Groove end projecting | 3 | |

Circular Corrugated Metal Pipe | Headwall | 4 |

Mitered to slope | 5 | |

Projecting | 6 | |

Circular Pipe, Beveled Ring Entrance | 45 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 Bevel | 45 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 Box | 90 deg. headwall | 27 |

Thick wall projecting | 28 | |

Thin wall projecting | 29 | |

Horizontal Ellipse Concrete | Square edge with headwall | 30 |

Grooved end with headwall | 31 | |

Grooved end projecting | 32 | |

Vertical Ellipse Concrete | Square edge with headwall | 33 |

Grooved end with headwall | 34 | |

Grooved end projecting | 35 | |

Pipe Arch, 18" Corner Radius, Corrugated Metal | 90 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 Metal | Projecting | 42 |

No bevels | 43 | |

33.7 deg. bevels | 44 | |

Arch, Corrugated Metal | 90 deg. headwall | 45 |

Mitered to slope | 46 | |

Thin wall projecting | 47 | |

Circular Culvert | Smooth tapered inlet throat | 48 |

Rough tapered inlet throat | 49 | |

Elliptical Inlet Face | Tapered inlet, beveled edges | 50 |

Tapered inlet, square edges | 51 | |

Tapered inlet, thin edge projecting | 52 | |

Rectangular | Tapered inlet throat | 53 |

Rectangular Concrete | Side tapered, less favorable edges | 54 |

Side tapered, more favorable edges | 55 | |

Slope tapered, less favorable edges | 56 | |

Slope tapered, more favorable edges | 57 |