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Publication Number: FHWARD99156 Date: August 2004 
a = blocked flow area by abutment
A = unobstructed flow area in approach channel
A_{f1} = blocked flow area in approachchannel floodplain
b = bridge pier width
B_{f} = width of floodplain in compound channel
B_{m} = width of main channel in compound channel
B_{m1} = width of approach main channel
B_{m2} = width of main channel in contracted section
C_{n} = units conversion coefficient used in equation 23
C_{0} = bestfit constant in proposed scour formula
C_{r} = bestfit coefficient in proposed scour formula
C_{LB} = livebed scour coefficient
d_{50} = median diameter of sediment
d_{s} = local scour depth
d_{sc} = theoretical long contraction scour depth
d_{st} = unsteady scour depth at any time t
F_{0} = approach value of densimetric grain Froude number in Lim scour formula
F_{1} = approachflow Froude number
F_{ab} = Froude number adjacent to abutment face
k = kepsilon refers to a numerical modeling technique that uses the ratio of turbulent kinetic energy squared to turbulent energy dissipation rate to define the eddy viscosity term for computations
k_{f} = spiralflow adjustment factor in Maryland scour formula
k_{s} = equivalent sandgrain roughness
k_{v} = velocity adjustment factor in Maryland scour formula
K_{1} = geometric shape factor for abutment in Froehlich scour formula
K_{2} = embankment skewness factor in Froehlich scour formula
K_{s}^{*} = abutment shape factor in Melville scour formula
K_{G} = channel geometric factor in Melville scour formula
K_{I} = flowintensity factor in Melville scour formula
K_{ST} = spillthrough abutment shape factor for scour formula in present study
K^{*} = abutment alignment factor in Melville scour formula
L_{a} = abutment/embankment length
M = discharge distribution factor in approach section = unblocked Q over total Q
= discharge contraction ratio for a bankline abutment
n = Manning's n
n_{fp} = Manning's n in floodplain of compound channel
n_{mc} = Manning's n in main channel of compound channel
n_{K} = Manning's n calculated from Keulegan's equation
N_{s} = sediment number (equivalent to densimetric grain Froude number)
N_{sc} = critical value of sediment number
q_{1} = flow rate per unit width in approach section in Maryland scour formula
q_{2} = flow rate per unit width in contracted section in Maryland scour formula
q_{bv} = volumetric sediment discharge per unit width
q_{f0} = flow rate per unit width in floodplain at normal depth (unconstricted)
q_{f0c} = critical flow rate per unit width in floodplain at normal depth (unconstricted)
q_{f1} = flow rate per unit width in the approach floodplain (constricted)
q_{f2} = flow rate per unit width in the contracted floodplain
q_{m1} = flow rate per unit width in the approach main channel at the beginning of scour
q_{m2} = flow rate per unit width in the contracted section in the main channel
Q = total discharge in compound channel
Q_{f1} = discharge in the approach floodplain
Q_{m0} = discharge in main channel for uniform flow in a compound channel
Q_{m1} = discharge in the approach main channel
Q_{m2} = discharge in the contracted main channel
Q_{obst1} = obstructed discharge in the approach section
R = channel hydraulic radius
SG = specific gravity of sediment
t = time since beginning of scour
t_{e} = time to reach equilibrium scour depth
u*_{1} = approach value of shear velocity = (_{1}/)^{0.5}
u*_{c} = critical value of shear velocity = (_{1}/)^{0.5}
V_{ab} = maximum resultant velocity near the upstream corner of the abutment face
V_{c} = critical velocity for initiation of motion
V_{f0} = floodplain velocity at normal depth
V_{f0c} = critical velocity for unconstricted floodplain depth of uniform flow
V_{f1} = bridge approach velocity in floodplain of compound channel
V_{f2} = floodplain velocity in the contracted floodplain after scour
V_{m0c} = critical velocity for the unconstricted depth in the main channel
V_{m1} = bridge approach velocity in main channel of compound channel
V_{m2c} = critical velocity in the main channel at the contracted section at equilibrium scour
V_{x} = mean contraction velocity in GKY scour formula
V_{R} = resultant velocity adjacent to tip of abutment in GKY scour formula
V_{1} = bridge approach velocity in rectangular channel
y = generic symbol for depth of flow in main channel or floodplain for calculating critical velocity
y_{ab} = depth near the upstream corner of the abutment face
y_{f0} = normal depth in floodplain
y_{f1} = bridge approach depth in floodplain of compound channel, including backwater
y_{ftw} = tailwater depth in floodplain
ym0 = normal depth in main channel
y_{m1} = bridge approach depth in main channel of compound channel, including backwater
y_{m2} = depth of flow in main channel in contracted section at equilibrium scour
y_{sc} = total depth of flow after scour, including the contraction scour depth only (Maryland formula)
y_{1} = bridge approach depth in rectangular channel
y_{2} = total flow depth in contracted section after scour (Maryland formula)
y' = vertical coordinate measuring distance above the mainchannel bed
y'/y_{m}= ratio of distance above the mainchannel bed to depth of the flow in the main channel
= specific weight of fluid
s = specific weight of sediment
f = general discharge per unit width contraction ratio for the floodplain
= ratio of boundary shear force to streamwise component of weight
= angle of repose of sediment
= fluid density
s = sediment density
= ratio of Manning's n in the main channel with compoundchannel flow to the value for the flow in the main channel alone
g = geometric standard deviation of sediment grain size distribution
c = critical shear stress for initiation of sediment motion
0 = average bed shear stress in uniform flow
1 = bed shear stress in approach flow
* = Shields' parameter, /[(s  ) d_{50}]
*_{c} = critical value of Shields' parameter, c/[(s  ) d_{50}]
*1 = Shields' parameter in approach flow section
*2 = Shields' parameter in contracted flow section
= independent dimensionless ratio in proposed scour formula = q_{f1}/Mq_{f0c}
Topics: research, infrastructure, hydraulics Keywords: research, infrastructure, hydraulics, Bridge scour, abutment scour, compound channels TRT Terms: research, hydraulics, hydrology, fluid mechanics, earth sciences, geophysics Updated: 04/23/2012
