Page 267 - Formulas and Calculations for Petroleum Engineering

260 Formulas and calculations for petroleum engineering

5.4 Average velocity of flow through a circular tube

Input(s)
P o : Pressure at Initial Point (Pa)
P L : Pressure at Point L (Pa)
R: Radius (m)
m: Viscosity (kg/(ms))
L: Length (m)

Output(s)
v z : Average Velocity (m/s)
v z,max : Maximum Velocity (Occurs at R ¼ 0) (m/s)

Formula(s)

ð P P Þ R 2
L
o
v ¼
z
8 m L
ð P P Þ R 2
o
L
v ¼
z,max
4 m L
Reference: Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons.,
Chapter: 2, Page: 51.
5.5 Average velocity of flow through an annulus
Input(s)

P o : Pressure at Initial Point (Pa)
P L : Pressure at Point L (Pa)
R: Radius (m)
m: Viscosity (kg/(ms))
L: Length (m)
k: Ratio of Inner Pipe’s Radius to Outer Pipe’s Radius (fraction)

Output(s)
v z : Average Velocity (m/s)

Formula(s)

2 3
2
ð P P Þ R 2 6 1 k 4 1 k 7
L
o
v ¼ 6 7
z 2
8 m L 4 1 k 1 5
ln
k
Reference: Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second ed.). John Wiley & Sons,
Chapter: 2, Page: 55.