b is the pier width. 
is the effective pier width defined as 
b_{1 }is the bottom width in the uncontracted
section. 
b_{2 }is the bottom width in the contracted
section. 
c_{a }is the pier location code in
the Arkansas pier scour equation, c_{a}=
0 for main channel piers and c_{a}= 1 for
piers on the banks of the main channel or on the floodplain. 
D_{10 }is the grain size of
bed material for which 10 percent is finer. 
D_{16} is the grain size of
bed material for which 16 percent is finer. 
D_{35 }is the grain size of
bed material for which 35 percent is finer. 
D_{50 }is the grain size of
bed material for which 50 percent is finer; the median grain size. 
D_{84 }is the grain size of
bed material for which 84 percent is finer. 
D_{90 }is the grain size of
bed material for which 90 percent is finer. 
D_{95 }is the grain size of
bed material for which 95 percent is finer. 
D_{99 }Is the grain size of bed material
for which 99 percent is finer. 
D_{i}or Dis the grain size
of bed material for which i or x percent is finer. 
D_{m }is the mean grain size of the
bed material. 
DA is the drainage area. 
D_{CFM }is an average of the coarse
grain sizes used by Molinas; see table 3.^{(1)} 
E_{b}is the exponent on the ratio of
bottom widths for live bed contraction scour equation. 
E_{n}is the exponent on the ratio of
roughness coefficients or live bed contraction scour equation. 
E_{Q }is the exponent on the ratio
of discharges for live bed contraction scour equation. 
f ( ) is an undefined function of parameters
enclosed in parentheses. 
F &F_{o}is the flow Froude
number defined as V_{o}/(gy_{o})^{0.5}. 
F_{p }is the pier Froude number defined
as V_{o}/(gb)^{0.5}. 
G is the acceleration of gravity. 
kis the standard normal deviate
of i. 
K is a multiplying factor that varies from
1.3 to 2.3 
K_{d } is a coefficient to correct
for sediment size by Melville and Sutherland.^{(2)} 
K_{i } is a coefficient to correct
the HEC18 equation for sediment size by Molinas; see table 3.^{(1)} 
K_{I }is a coefficient to correct for
flow intensity defined by Melville and Sutherland.^{(2)} 
K_{s }is a coefficient to correct for
pier shape defined by Melville and Sutherland.^{(2)} 
K_{sc }is a coefficient for pier shape
in the Simplified Chinese equation, defined by Gao et al. to be 1 for
cylinders, 0.8 for roundnosed piers, and 0.66 for sharp nosedpiers.^{(3)} 
K_{S}_{2 }is a coefficient
for pier shape used by Larras and is 1.0 for cylindrical piers and 1.4
for rectangular piers.^{(4)} 
K_{u }is 1.0 for SI units and 1.81
for customary English units in the critical velocity equation. 
K_{y }is a coefficient to correct for
flow depth defined by Melville and Sutherland.^{(2)} 
K_{1 }is a coefficient based
on the shape of the pier nose, defined as 1.1 for squarenose piers,
1.0 for circular or roundnosed piers, 0.9 of sharpnosed piers, and
1.0 for a group of cylinders. 
K_{2 }is a coefficient to
correct for the skew of the pier to the approach flow, defined as (cos
α + (L/b)sin α)^{0.65}.

K_{3 }is a coefficient to
correct for the channel bed condition, defined as 1.1 except when medium
to large dunes are present, and then it can range from 1.2 to 1.3. 
K_{4} is a coefficient to
correct for bed material size and gradation; see table 3. 
K4MuK_{4} coefficient
derived by Mueller.^{(5) } 
K4MoK_{4} coefficient
derived by Molinas.^{(1)} 
is a coefficient to correct for flow
alignment defined by Melville and Sutherland (1988).^{(2)} 
is a coefficient to correct for flow
alignment defined by Melville and Sutherland (1988).^{(2)} 
L is the length of the pier. 
Q_{1}is the discharge in the uncontracted
section. 
Q_{2 }is the discharge in the contracted
section. 
S is the slope of channel in the vicinity of
the bridge. 
V_{o }is the approach velocity for
pier scour. 
V_{c }is the critical (incipienttransport)
velocity for the D_{50 }size particle. 
V_{cx }is the critical (incipienttransport)
velocity for the D_{x} size particle. 
V_{R }is a velocity intensity term
used by Richardson and Davis; see table 3.^{(6)} 
is the approach velocity corresponding to critical velocity and incipient
scour of the D_{50} in the accelerated flow region
at the pier. 
is the approach velocity corresponding to critical velocity and incipient
scour of the D_{x} in the accelerated flow region at
the pier. 
V_{i} is the approach velocity corresponding
to critical velocity and incipient scour in the accelerated flow region
at the pier defined by Molinas; see table 3.^{(1)} 
V_{cm }is the critical (incipienttransport)
velocity for the coarse size fraction defined by Molinas; see table
3.^{(1)} 
V_{LP }is the live bed peak
velocity defined by Sheppard.^{(7)} 
V_{2 } is the velocity in
the contracted section. 
y_{o }is the approach depth of flow
for pier scour. 
y_{s }is the depth of scour. 
Y_{1 }is the depth in the uncontracted
section. 
Y_{2 }is the depth in the contracted
section. 
α is the skew of the pier to approach
flow. 
ф is a pier shape factor in Froelich's
equations 
σ is the coefficient of gradation. 
θ is the Shield's parameter. 
τ represents one or more shear stress
variables. 
ν is the kinematic viscosity in Shen's
equation (ft^{2}/sec). 