61Hydrodynamics of Pneumatic Foam
g Acceleration due to gravity [m.s
−2
]
j
d
Supercial liquid drainage velocity [m.s
−1
]
j
f
Supercial liquid velocity up the column [m.s
−1
]
j
f
*
Liquid supercial velocity at the ooding condition [m.s
−1
]
j
g
Supercial gas velocity [m.s
−1
]
j
g
*
Supercial gas velocity at the ooding condition [m.s
−1
]
k Pre-factor in Equation (3.20) [kg.m
−1
.s
n−2
]
m Dimensionless number used in Equation 3.2 [–]
n Dimensionless index used in Equation 3.2, or index in Equation 3.20 [–]
p Pressure [N.m
−2
]
Q
g
Volumetric gas ow rate [m
3
.s
−1
]
r
b
Bubble radius [m]
Sk Stokes number dened in Equation 3.1 [–]
U
S
Slip velocity at the pipe wall [m.s
−1
]
x Length, measured positive upward, or in horizontal direction [m]
Greek