Page 274 - Formulas and Calculations for Petroleum Engineering

Fluid flow and transport phenomena formulas and calculations Chapter 5 267

5.20 Darcy Weisbach equation (head loss form)

Input(s)
L: Length of the Pipe (m)
2
g: Acceleration due to Gravity (m/s )
V: Average Velocity of the Fluid Flow, Equal to the Volumetric Flow Rate per Unit Cross-sectional
Wetted Area (m/s)
D: Hydraulic Diameter of the Pipe (For a Pipe of Circular Section, this Equals the Internal Diameter of the Pipe) (m)
f D : Dimensionless Coefficient Called the Darcy Friction Factor (dimensionless)

Output(s)
Dh: Head Loss Due to Friction (m)

Formula(s)

1 V 2
Dh ¼ f
D
2 g D
Reference: Wikipedia.org.

5.21 Darcy Weisbach equation (pressure loss form)
Input(s)

L: Length of the Pipe (m)
3
r: Density of Fluid (kg/m )
V: Average Velocity of the Fluid Flow, Equal to the Volumetric Flow Rate per Unit Cross-sectional
Wetted Area (m/s)
L: Lift Force (Newton)
D: Hydraulic Diameter of the Pipe (for a Pipe of Circular Section, equals the Internal Diameter of the Pipe) (m)
f D : Dimensionless Coefficient Called the Darcy Friction Factor (dimensionless)

Output(s)

DP: Pressure Loss due to Friction (m)

Formula(s)

2
V
r
DP ¼ L f
D
2 D
Reference: Wikipedia.org.

5.22 Dean number

Input(s)
3
r: Density of the Fluid (kg/m )
m: Dynamic Viscosity (kg/ms)
V: Axial Velocity Scale (m/s)
d: Diameter (m)
R c : Radius of Curvature of the Path of Channel (m)