Skip to content

NCHRP Report 734: Hydraulic Loss Coefficients for Culverts

Reference:

  • Title: Hydraulic Loss Coefficients for Culverts
  • Report: NCHRP Report 734
  • Publisher: Transportation Research Board
  • Year: 2012

1. Overview

NCHRP 734 expands on the traditional hydraulic design of highway culverts by providing empirically derived loss coefficients for modern geometries, specifically addressing:

  1. Slip-lined culverts
  2. Buried-invert (embedded) culverts
  3. Multi-barrel culvert installations

2. Slip-Lined Culverts

Entrance Loss Coefficients ($K_e$)

Slip-lined culverts typically result in a projecting pipe inlet condition because the smaller liner pipe extends beyond the original host pipe. The report provides the following entrance loss coefficients for slip-lined conditions (derived from Table 3-1):

  • Traditional thin-wall projecting: $K_e = 0.80$
  • Slip-lined, untapered: average $K_e = 0.77$
  • Slip-lined, tapered 2-in. projection: $K_e = 0.71$
  • Slip-lined, tapered 4-in. projection: $K_e = 0.70$

The report gives approximately 1.5% uncertainty for these measurements. Source: Chapter 3 results, printed page 22 (local PDF page 30).

Inlet Control Constants

Derived from Table 3-2 for Form 1 and Form 2 HDS-5 unsubmerged/submerged equations:

Test Culvert Inlet End Treatment Unsubmerged Form 1 (c, Y) Unsubmerged Form 2 (K, M) Submerged
Traditional projecting c = 0.0946, Y = 0.60 K = 0.5812, M = 0.58 c = 0.0513, Y = 0.69
Slip-lined, 2-in. projecting c = 0.0971, Y = 0.55 K = 0.5830, M = 0.57 c = 0.0520, Y = 0.64
Slip-lined, 4-in. projecting c = 0.0945, Y = 0.54 K = 0.5808, M = 0.57 c = 0.0520, Y = 0.66
Slip-lined, tapered 2-in. projection c = 0.0908, Y = 0.54 K = 0.5772, M = 0.57 c = 0.0467, Y = 0.69
Slip-lined, tapered 4-in. projection c = 0.0841, Y = 0.52 K = 0.5697, M = 0.56 c = 0.0473, Y = 0.65

Source locator: Table 3-2, printed page 23 (local PDF page 31). The final row label is printed as a duplicate of the tapered 2-in. row. The narrative on printed page 22 (local PDF page 30) identifies Ke = 0.70 as the tapered 4-in. projection, and the four-end-treatment sequence confirms that interpretation. Preserve the source typo in review notes; use an explicitly named 4-in record if implemented.

Observation: Under inlet control, there is no appreciable difference between the head-discharge relationships for the traditional thin-wall projecting inlet and the slip-lined thin-wall projecting inlet.

3. Multi-Barrel Interactions

The report found that a representative average-barrel relationship correlated well with single-barrel results and concluded that superposition is likely appropriate for most total-flow calculations. Nonuniform approach flow produced differences up to about 10%, and a depressed barrel up to about 4%. Individual middle-barrel discharge could differ by about 7% (and barrels in a two-barrel test by about 5%), which matters for barrel-specific outlet protection or fish passage. Source: Chapter 5 conclusions, printed page 49 (local PDF page 57).

4. Applicability to the Repository

  • Slip-lined configurations should be added to the inlet configuration catalogue with their associated $K_e$ and inlet control regression constants.
  • Embedded culverts (composite roughness) will require a new primary or formally corrected basis if the domain model expands to natural-bottom or partially buried culverts. Do not implement original NCHRP Table 2-5 coefficients.
  • Multi-barrel superposition remains a reasonable total-flow architecture for CulvertCrossing; document the approach-flow and per-barrel limitations rather than applying an unsupported blanket efficiency reduction.
  • Chapter 4's Borda-Carnot exit-loss refinement requires downstream channel area and a sudden-expansion context. It is not a drop-in replacement for the current reservoir/ pool Ko = 1.0 assumption.
  • Chapters 7 and 8 show depth-dependent roughness and substantial uncertainty in composite-roughness methods. No composite value may be inferred from a single material enum; CS-030 owns any future context-rich implementation.

5. Embedded-coefficient correction

Eric J. Jones's 2019 HY-8 developer note Reviewing Coefficients in Embedded Circular Culverts from NCHRP Report 734 is available locally (PDF pages 1–14 for the method and conclusions). It reports two defects in the Chapter 2 research data:

  • A D^0.5 was computed incorrectly, corrupting the dimensionless discharge; and
  • the 50% embedded, beveled-inlet series contained false and insufficient data.

The note recovers a replacement 50% beveled dataset and recalculates dimensionless flow. It then adds synthetic high-flow points based on the ratio to HY-8's unembedded curve so a fifth-order polynomial remains stable beyond the experiment. That extension is a documented HY-8 implementation choice, not primary experimental evidence. Consequently, original NCHRP embedded coefficients are rejected for executable use, while the note's adjusted polynomials are retained only as version-history/comparison evidence. CS-032 requires a formally supportable method decision before adding embedded culverts.