Inlet head loss depends on the geometry of the inlet edge. This loss is expressed as the barrel velocity head reduced by a factor known as the entrance head loss coefficient, Ke.

Where:

V = Velocity in the barrel (ft/s)

g = Acceleration due to gravity

The entrance loss coefficient, Ke, is the head loss term of the energy equation for open-channel flow.  The head loss coefficient is a measure of the efficiency of the inlet to smoothly transition flow from the upstream channel into the culvert.  Although it is typically reported as a constant, it does vary with flow.  Typically, reported Ke values are for near or full flow conditions.  Under fish passage flows, Ke values are often substantially less.

The coefficient can range in value between 0 and 1.  Larger head loss coefficients are associated with increased flow contraction in the inlet zone.  Culverts having a width less than the upstream channel will constrict flow and can create a steep drop in the water surface profile at the inlet, often resulting in a velocity barrier for fish attempting to exit the culvert.

The entrance loss coefficient is a function of the flow.  Coefficients are often supplied by culvert manufacturers and are for relative depths (headwater depth/culvert rise) of about 1.2, well above fish passage flows.

Attempts should be made to minimize the head loss at the culvert inlet to improve passage.  Sizing the culvert large enough to avoid constricting the flow will result in a inlet head-loss coefficient of 0 for fish passage flows.  Another means of reducing the head-loss at the inlet is to build wingwalls to direct the flow smoothly into the culvert.

Bates (1992) suggests that inlet coefficients should not exceed 0.7 for adult salmonid fish passage, 0.5 for sites with marginal passage conditions, and 0.2 for juvenile salmonid passage.

Entrance Loss Coefficients for Pipe or Pipe Arch Culverts

 Type of Culvert and Inlet Design Coefficient, Ke Concrete Pipe Projecting from Fill (no headwall) Square cut end 0.5 Socket end 0.2 Concrete Pipe with Headwall and/or Wingwall Square cut end 0.5 Socket end (grooved end) 0.2 Rounded entrance (radius = 1/12 of diameter) 0.2 Concrete Pipe Mitered to conform to fill slope 0.7 End section conformed to fill slope 0.5 Beveled edges, 33.7 or 45 degree bevels 0.2 Side slope tapered inlet 0.2 Corrugated Metal Pipe or Pipe Arch Projecting form fill (no headwall) 0.9 Mitered (beveled to conform to fill slope) 0.7 Headwall or headwall with square edge wingwalls 0.5 End section conforming to fill slope 0.5 Beveled Ring 0.25 Headwall, rounded edge 0.2

Entrance Loss Coefficients for Reinforced Concrete Box Culverts

 Type of Culvert and Inlet Design Coefficient, Ke Headwall Parallel to Embankment (no wingwalls) Square edged on three edges 0.5 Three edges rounded  (radius = 1/12 barrel dimension) 0.2 Wingwalls at 30 to 75 degrees to Barrel Square edged at crown 0.4 Top corner rounded to radius of 1/12 barrel 0.2 Wingwalls at 10 to 25 degrees to Barrel Square edged at crown 0.5 Corrugated Metal Pipe or Pipe Arch Square edged at crown 0.7 Side or slope tapered inlet 0.2