Fluid Flow Table of Contents
Hydraulic and Pneumatic Knowledge
Fluid Power Equipment
Pressure drop in pipes is caused by:
 Friction
 Vertical pipe difference or elevation
 Changes of kinetic energy
 Calculation of pressure drop caused by friction in circular pipes
To determine the fluid (liquid or gas) pressure drop along a pipe or pipe component, the following calculations, in the following order.
Equation Reynolds Number:
Re = ω D / v
Re = ρ v l / µ
Re = ω l / v 
Where:
Re = Reynolds Number (unitless)
ω = Velocity of fluid flow (m/sec)
D = Diameter of Pipe (m)
v = Kinematic Viscosity (m^{2}/s)
ρ = Density of fluid (kg/m^{3})
l = Characteristic length, thoe chord of an airfoil
Kinematic Viscosity
Example kinematic viscosity values for air and water at 1 atm and various temperatures.
Air Kinematic Viscosity m^{2}/a
1.2462E5 
10 
14 
1.3324E5 
0 
32 
1.4207E5 
10 
50 
1.5111E5 
20 
68 
Water Kinematic Viscosity m^{2}/ a
1.6438E6 
1 
33.8 
1.267E6 
10 
50 
9.7937E7 
20 
6 
Kinematic Viscosity Table Chart of Liquids 
If the Reynolds number < 2320, than you have laminar flow.
Laminar flow is characterized by the gliding of concentric cylindrical layers past one another in orderly fashion. The velocity of the fluid is at its maximum at the pipe axis and decreases sharply to zero at the wall. The pressure drop caused by friction of laminar flow does not depend of the roughness of pipe.
If the Reynolds number > 2320, you have turbulent flow.
There is an irregular motion of fluid particles in directions transverse to the direction of the main flow. The velocity distribution of turbulent flow is more uniform across the pipe diameter than in laminar flow. The pressure drop caused by friction of turbulent flow depends on the roughness of pipe.
Select pipe friction Coefficient:
The pipe friction coefficient is a dimensionless number. The friction factor for laminar flow condition is a function of Reynolds number only, for turbulent flow it is also a function of the characteristics of the pipe wall.
Determine Pipe friction coefficient at laminar flow:
λ = 64 / Re
Where:
λ = Pipe Friction Coefficient
Re = Reynolds number
Note: Perfectly smooth pipes will have a roughness of zero.
Determine Pipe friction coefficient at turbulent flow (in the most cases) Colbrook Equation:
or
Where:
= Pipe Friction Coefficient
g = Acceleration of Gravity (9.8 m/s/s) Re = Reynolds Number (unitless)
k = Absolute Roughness (mm)
D = Diameter of Pipe (m)
lg = Short for Log
The solutions to this calculation is plotted vs. the Reynolds number to create a Moody Chart.
Following table gives typical roughness values in millimeters for commonly used piping materials.
Surface Material 
Absolute Roughness Coefficient  k (mm) 
Aluminum, Lead 
0.001  0.002 
Drawn Brass, Drawn Copper 
0.0015 
Aluminum, Lead 
0.001  0.002 
PVC, Plastic Pipes 
0.0015 
Fiberglass 
0.005 
Stainless steel 
0.015 
Steel commercial pipe 
0.045  0.09 
Stretched steel 
0.015 
Weld steel 
0.045 
Galvanized steel 
0.15 
Rusted steel 
0.15  4 
Riveted steel 
0.9  9 
New cast iron 
0.25  0.8 
Worn cast iron 
0.8  1.5 
Corroding cast iron 
1.5  2.5 
Asphalted cast iron 
0.012 
Galvanized iron 
0.015 
Smoothed cement 
0.3 
Ordinary concrete 
0.3  3 
Well planed wood 
0.18  0.9 
Ordinary wood 
5 
Determine Pressure drop in circular pipes:
Where:
Δp = Pressure Drop (Pa or kg / ms ^{2})
λ = Pipe Friction Coefficient
L = Length of Pipe (m)
D = Pipe Diameter (m)
p = Density (kg/m^{3})
ω = Flow Velocity (m/s)
If you have valves, elbows and other elements along your pipe then you calculate the pressure drop with resistance coefficients specifically for the element. The resistance coefficients are in most cases found through practical tests and through vendor specification documents. If the resistance coefficient is known, than we can calculate the pressure drop for the element.
Where:
= Pressure Drop (kg/m^{2})
= Resistance Coefficient (determined by test or vendor specification)
p = Density (kg/m^{3})
ω = Flow Velocity
Pressure drop by gravity or vertical elevation
Where:
Δp = Pressure Drop
(kg/m^{2})
p = Density (kg/m^{3})
g = Acceleration of Gravity (9.8 m/s/s)
ΔH = Vertical Elevation or Drop
(m)
Pressure drop of gasses and vapor
Compressible fluids expands caused by pressure drops (friction) and the velocity will increase. Therefore is the pressure drop along the pipe not constant.
Where:
p_{1} = Pressure incoming (kg/m^{2})
T_{1} = Temperature incoming (°C)
p_{2} = Pressure leaving (kg/m^{2})
T_{2} = Temperature leaving (°C)
We set the pipe friction number as a constant and calculate it with the inputdata. The temperature, which is used in the equation, is the average of entrance and exit of pipe.
Note: You can calculate gases as liquids, if the relative change of density is low (change of density/density = 0.02).
