a = blocked flow area by abutment

A = unobstructed flow area in approach channel

A_{f1} = blocked flow area in approach-channel 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} = best-fit constant in proposed scour formula

C_{r} = best-fit coefficient in proposed scour formula

C_{LB} = live-bed 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} = approach-flow Froude number

F_{ab} = Froude number adjacent to abutment face

k- = k-epsilon 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} = spiral-flow adjustment factor in Maryland scour formula

k_{s} = equivalent sand-grain 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} = flow-intensity factor in Melville scour formula

K_{ST} = spill-through 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 main-channel bed

y'/y_{m}= ratio of distance above the main-channel 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 compound-channel 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}

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