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## Introduction to Highway Hydraulics

List of Tables

List of Figures

List of Symbols

A = Cross sectional area, or drainage area
B = Bottom width of a channel
C = Runoff coefficient in Rational Method
D = Culvert diameter or sediment size
D50 = Sediment size for which 50 percent by weight of the particles are smaller; similarly D65, D84, D90 represent sizes for which 65, 84, and 90 percent of the particles are smaller
Fr = Froude Number
f = Darcy Weisbach friction factor
g = Acceleration due to gravity, 9.81 m/s2 (32.2 ft/s2)
H = Specific energy
Hf = Friction loss of head
i = Rainfall intensity, mm/h (in/hr)
K = Conveyance
ks = Height of roughness channels
Ku = Correction factor for units: SI (English)
n = Manning's resistance coefficient
P = Wetted perimeter of the flow
Q = Discharge (flow rate)
q = Unit discharge
Re = Reynolds Number
rc = Radius of curvature at the center of the stream
ri, ro = Radius of curvature for inner and outer banks in a bend
S = Channel slope
Sf = Friction slope (also called the energy slope)
So = Bed slope
Sw = Slope of water surface
T = Top width
V = Velocity
V* =
 Shear velocity, τo/ρ
X = Coordinate axis
y = Coordinate axis, depth of flow
yc = Critical depth of flow
ys = Scour depth
Z = Elevation above arbitrary reference level (and Side slope of channel bank)

Greek Symbols

 α = Energy correction factor β = Momentum correction factor γ = Specific weight of water, 9810 N/m3 (62.4 lbs/ft3) λ = Wave length μ = Dynamic viscosity of a fluid ν = Kinematic viscosity of a fluid ρ = Fluid density, water = 1,000 kg/m3 (1.94 slugs/ft3) ρs = Density of sediment particles τ = Shear stress τo = Bed shear stress τc = Critical shear stress of sediment particles

### Listing of Updates and Corrections (errata & corrigenda)

DATE ACTION BY
20 Aug 2012

Page 4-43, Example Problem 4.8 (SI Units): sequent depth (y2) equation is incorrect (i.e., "- 1" is within the square root). The proper form of the equation is:

The solution of 3.73 m is correct.

JSK
20 Aug 2012

Page 4-43, Example Problem 4.8 (English Units): velocities should be 54.7 ft/s (not 49 ft/s) on steep slope and 5.6 ft/s (not 5.51 ft/s) on mild slope:

"... velocity on the steep slope were calculated to be 1.0 ft and 54.7 ft/s ..."

"... the ... velocity were calculated to be 9.71 ft and 5.6 ft/s ..."

The figure depicting the steep slope to mild slope transition also lists the incorrect velocities. They should be using the correct velocities noted above.

The error is a result of conversion errors between the SI and English units within Example Problem 4.8. The SI version of the example has correct velocities.

JSK
20 Aug 2012

Page 4-44, Example Problem 4.8 (English Units): The Froude equation uses the incorrect velocity (see above). This results in an incorrect Froude value.

Using 54.7 ft/s, the correct Froude number equals 9.64.

JSK
20 Aug 2012

Page 4-44, Example Problem 4.8 (English Units): sequent depth (y2) equation is incorrect (i.e., "- 1" is within the square root). The proper form of the equation is:

As the correct solution is 13.14 ft, in the last paragraph of this section, the text should read " ... normal depth (i.e., 13.14 > 9.71) ...". The channel water surface still exhibits an M3 curve.

JSK

This list includes all known items as of Monday 20 August 2012

Notes:

• 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