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Hydraulic Design of Energy Dissipators for Culverts and Channels
Hydraulic Engineering Circular Number 14, Third Edition

PDF Version (3.2 MB)


First Edition

The first edition of this Circular was prepared in 1975 as an integral part of Demonstration Project No. 31, "Hydraulic Design of Energy Dissipators for Culverts and Channels," sponsored by Region 15. Mr. Philip L. Thompson of Region 15 and Mr. Murray L. Corry of the Hydraulics Branch wrote sections, coordinated, and edited the Circular. Dr. F. J. Watts of the University of Idaho (on a year assignment with Hydraulics Branch), Mr. Dennis L. Richards of the Hydraulics Branch, Mr. J. Sterling Jones of the Office of Research, and Mr. Joseph N. Bradley, Consultant to the Hydraulics Branch, contributed substantially by writing sections of the Circular. Mr. Frank L. Johnson, Chief, Hydraulics Branch, and Mr. Gene Fiala, Region 10 Hydraulics Engineer, supported the authors by reviewing and discussing the drafts of the Circular. Mr. John Morris, Region 4 Hydraulics Engineer, collected research results and assembled a preliminary manual that was used as an outline for the first draft. Mrs. Linda L. Gregory and Mrs. Silvia M. Rodriguez of the Region 15 Word Processing center and Mrs. Willy Rudolph of the Hydraulics Branch aided in manual preparation. The authors wish to express their gratitude to the many individuals and organizations whose research and designs are incorporated into this Circular.

Second Edition

Mr. Philip Thompson and Mr. Dennis Richards updated the first edition in 1983 so that HEC 14 could be reprinted and distributed as a part of Demonstration Project 73. The 1983 edition did not add any new dissipators, but did correct all the identified errors in the first edition. A substantial revision for Chapter 5, Estimating Erosion at Culvert Outlets, was accomplished using material that was published by Dr. Steven Abt, Dr. James Ruff, and Dr. A Shaikh in 1980. The second edition was prepared in U.S. customary units.

Third Edition

Mr. Philip Thompson and Mr. Roger Kilgore prepared this third edition of the Circular with the assistance of Dr. Rollin Hotchkiss. This edition retains all of the dissipators featured in the second edition, except the Forest Service (metal), USBR Type II stilling basin, and the Manifold stilling basin. The following dissipators have been added: USBR Type IX baffled apron, riprap aprons, broken-back culverts, outlet weir, and outlet drop followed by a weir. This edition is in both U.S. customary and System International (SI) units. A previous SI unit version of HEC 14 was published in 2000 as a part of the FHWA Hydraulics Library on CDROM, FHWA-IF-00-022.

Table of Contents

List of Tables

List of Figures

List of Symbols

  • a = Acceleration, m/s2 (ft/s2)
  • A = Area of flow, m2 (ft2)
  • Ao = Area of flow at culvert outlet, m2 (ft2)
  • B = Width of rectangular culvert barrel, m (ft)
  • D = Diameter or height of culvert barrel, m (ft)
  • D50 = Particle size of gradation, of which 50 percent, of the mixture is finer by weight, m (ft)
  • E = Energy, m (ft)
  • f = Darcy-Weisbach resistance coefficient
  • F = Force, N (lb)
  • Fr = Froude number, ratio of inertial forces to gravitational force in a system
  • g = gravitational acceleration, m/s2 (ft/s2
  • HL = Head loss (total), m (ft)
  • Hf = Friction head loss, m (ft)
  • n = Manning's flow roughness coefficient
  • P = Wetted perimeter of flow prism, m (ft)
  • q = Discharge per unit width, m2/s (ft2/s)
  • Q = Discharge, m3/s (ft3/s)
  • r = Radius
  • R = Hydraulic radius, A/P, m (ft)
  • Re = Reynolds number
  • S = Slope, m/m (ft/ft)
  • Sf = Slope of the energy grade line, m/m (ft/ft)
  • So = Slope of the bed, m/m (ft/ft)
  • Sw = Slope of the water surface, m/m (ft/ft)
  • T = Top width of water surface, m (ft)
  • TW = Tailwater depth, m (ft)
  • V = Mean Velocity, m/s (ft/s)
  • Vn = Velocity at normal depth, m/s (ft/s)
  • y = Depth of flow, m (ft)
  • ye = Equivalent depth (A/2)1/2, m (ft)
  • ym = Hydraulic depth (A/T), m (ft)
  • yn = Normal depth, m (ft)
  • yc = Critical depth, m (ft)
  • yo = Outlet depth, m (ft)
  • Z = Side slope, sometimes expressed as 1:Z (Vertical:Horizontal)
  • α = Unit conversion coefficient (varies with application)
  • α = Kinetic energy coefficient; inclination angle
  • β = Velocity (momentum) coefficient; wave front angle
  • γ = Unit Weight of water, N/m3 (lb/ft3)
  • θ = Angle: inclination, contraction, central
  • μ = Dynamic viscosity, N·s/m2 (lb·s/ft2)
  • ν = Kinematic viscosity, m2/s (ft2/s)
  • ρ = Mass density of fluid, kg/m3 (slugs/ft3)
  • τ = Shear stress, N/m2 (lb/ft2)


  • Basin: Depressed or partially enclosed space.
  • Customary Units (CU): Foot-pound system of units also referred to as English units.
  • Depth of Flow: Vertical distance from the bed of a channel to the water surface.
  • Design Discharge: Peak flow at a specific location defined by an appropriate return period to be used for design purposes.
  • Freeboard: Vertical distance from the water surface to the top of the channel at design condition.
  • Hydraulic Radius: Flow area divided by wetted perimeter.
  • Hydraulic Roughness: Channel boundary characteristic contributing to energy losses, commonly described by Manning's n.
  • Normal Depth: Depth of uniform flow in a channel or culvert.
  • Riprap: Broken rock, cobbles, or boulders placed on side slopes or in channels for protection against the action of water.
  • System International (SI): Meter-kilogram-second system of units often referred to as metric units.
  • Uniform flow: Hydraulic condition in a prismatic channel where both the energy (friction) slope and the water surface slope are equal to the bed slope.
  • Velocity, Mean: Discharge divided by the area of flow.

Listing of Updates and Corrections (errata & corrigenda)

Date Action By
13 Aug 2012Page 4-2, first paragraph: text should have parentheses around the '3Fr' quantity:"

... if the tanθ is greater than 1/(3Fr), ..."

1 Oct 2012Page 4-2 Figure 4.2 Blaisdell's (1/3Fr) should be Blaisdell's (1/(3Fr))CLN
13 Aug 2012Page 4-4, Equation 4.3 should be:

"θ = tan-1(1/(3Fr))"

13 Aug 2012Page 4-4, third paragraph: text should have parentheses around the '3Fr' quantity:

"... flaring the wingwall more than 1/(3Fr) (for example 45°) ..."

13 Aug 2012Page 4-5, Step 3: equation should depict:

"tanθ = 1/(3Fr) = 1/(3(1.52)) = 0.22"

1 Oct 2012Page 4-6, Alternative 2 ... tanθ = 1/3Fr should be tanθ = 1/(3Fr)CLN
13 Aug 2012Page 4-7, Step 3: equation should depict:

"tanθ = 1/(3Fr) = 1/(3(1.52)) = 0.22"

1 Oct 2012age 4-8, Alternative 2 ... tanθ = 1/3Fr should be tanθ = 1/(3Fr)CLN

This list includes all known items as of Monday 1 October 2012


  • No update to the publication is planned at this time.
  • FHWA does not have any printed copies of this document. NHI allows purchase of some FHWA documents. See the FHWA Hydraulics website to report any additional errata and corrigenda.
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Updated: 09/22/2014

United States Department of Transportation - Federal Highway Administration