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Hydraulics Engineering

 
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Introduction to Highway Hydraulics

Table of Contents




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
hL = Headloss
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
R = Hydraulic radius
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:

y sub 2 equals 0.33 divided by 2 times [ the square root of (1 plus 8 times 8.34 squared) minus 1] equals 3.73 m

 

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.

Profile sketch of Example Problem 4.8 in English Units as described in the text with potential water surface profiles S 1 and M 3 shown

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:

y sub 2 equals 0.33 divided by 2 times [ the square root of  (1 plus 8 times 8.34 squared) minus 1] equals 3.73 m

 

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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Contact:

Veronica Ghelardi
Resource Center (Lakewood)
720-963-3240
veronica.ghelardi@dot.gov

Updated: 09/12/2012

FHWA
United States Department of Transportation - Federal Highway Administration