Page 268 - Formulas and Calculations for Petroleum Engineering

Fluid flow and transport phenomena formulas and calculations Chapter 5 261

5.6 Average velocity of fluids in flow of two adjacent immiscible fluids

Input(s)
P o : Pressure at Initial Point (Pa)
P L : Pressure at Point L (Pa)
b: Distance (m)
m I : Viscosity of Phase I, Denser, More Viscous Fluid (kg/(ms))
m II : Viscosity of phase II, Less Dense, Less Viscous Fluid (kg/(ms))
L: Length (m)

Output(s)
v zI : Average Velocity for Phase I (m/s)
v zII : Average Velocity for Phase II (m/s)

Formula(s)

ð P P Þ b 2 7 m + m II
I
o
L
v ¼
zI
12 m L
I m + m II
I
ð P P Þ b 2 m +7 m II
I
o
L
v ¼
zII
12 m L m + m II
I
II
Reference: Bird, R.B., Stewart, W.E., and Lightfoot, E.N. (2002). Transport Phenomena (Second ed.). John Wiley & Sons,
Chapter: 2, Page: 58.
5.7 Average velocity over the cross section of a falling film
Input(s)
3
r: Density (kg/m )
2
g: Gravitational Acceleration (m/s )
d: Film Thickness (m)
m: Viscosity (kg/(ms))
b: Angle of Inclination w.r.t Direction of Gravity (rad)
v z,max : The Maximum Velocity at x ¼ 0 (m/s)

Output(s)

v z : Average Velocity (m/s)

Formula(s)

2
r g d cos bðÞ
v ¼
z
3 m
Reference: Bird, R.B., Stewart, W.E., and Lightfoot, E.N. (2002). Transport Phenomena (Second ed.). John Wiley & Sons,
Chapter: 2, Page: 45.