§ 10.3.5. Energy Balance at Inlet

The culvert inlet headwater (HW _oc ) can be calculated using the energy Equation 10.3.5.a below. With the hydraulic grade line at the culvert entrance (calculated from section 10.3.4) the velocity head at the entrance (h _vi ) can be calculated.

(Equation 10.3.5.a)

HW _oc = H _i + h _vi + h _e − h _va

HW _oc = headwater depth due to outlet control (ft.)
h _va = velocity head of flow approaching the culvert entrance (ft.)
h _vi = velocity head in the entrance (ft.) (calculated using Equation 10.3.3.b)
h _e = entrance head loss (ft.) (calculated using Equation 10.3.5.b)
H _i = depth of hydraulic grade line just inside the culvert at inlet (ft.)

Generally the approach velocity of the upstream channel to the culvert inlet can be assumed to be zero (0), thus the headwater and energy grade line are equal. This is a conservative approach for a headwater depth. The design engineer can calculate the approach velocity and determine the appropriate headwater.

The entrance loss should be calculated using Equation 10.3.5.b on the following page.

(Equation 10.3.5.b)

h _e = entrance loss
C _e = entrance loss coefficient
V _i = flow velocity inside culvert inlet (fps)

The values of C _e are shown below on Table 10.3.5.

Table 10.3.5 - Entrance Loss Coefficients (C _e )
(Source FHWA "Hydraulic Design of Highway Culverts", 3 ^rd ed.)

Type of Structure and Design of Entrance	Coefficient C e
Pipe, Concrete
Projecting from fill, socket end (groove-end)	0.2
Projecting from fill, sq. cut end	0.5
Headwall or headwall and wingwalls
Socket end of pipe (groove-end)	0.2
Square-edge	0.5
Rounded (radius = D/12)	0.2
Mitered to conform to fill slope	0.7
End-Section conforming to fill slope	0.5
Beveled edges, 33.7° or 45° bevels	0.2
Side- or slope-tapered inlet	0.2
Pipe or Pipe-Arch Corrugated Metal
Projecting from fill (no headwall)	0.9
Headwall or headwall and wingwalls square-edge	0.5
Mitered to conform to fill slope, paved or unpaved slope	0.7
End-Section conforming to fill slope	0.5
Beveled edges, 33.7° or 45° bevels	0.2
Side- or slope-tapered inlet	0.2
Box, Reinforced Concrete
Headwall parallel to embankment (no wingwalls)
Square-edged on 3 edges	0.5
Rounded on 3 edges to radius of D/12 or B/12
or beveled edges on 3 sides	0.2
Wingwalls at 30° to 75° to barrel
Square-edged at crown	0.4
Crown edge rounded to radius of D/12 or beveled top edge	0.2
Wingwall at 10° to 25° to barrel
Square-edged at crown	0.5
Wingwalls parallel (extension of sides)
Square-edged at crown	0.7
Side- or slope-tapered inlet	0.2