Fluid Pressure Drop Along Pipe Length of Uniform Diameter

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:

Where:

Re = Reynolds Number

= Velocity of Flow

D = Diameter of Pipe

v = Kinematic Viscosity

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:

   

Where:

= 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):

   

Where:

= Pipe Friction Coefficient

g = Acceleration of Gravity

Re = Reynolds Number

k = Absolute Roughness

D = Diameter of Pipe

lg = Log

The solutions to this calculation is plotted vs. the Reynolds number to create a Moody Chart.


Determine Pressure drop in circular pipes:

   

Where:

= Pressure Drop

= Pipe Friction Coefficient

L = Length of Pipe

D = Pipe Diameter

p = Density

= Flow Velocity


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

= Resistance Coefficient (determined by test or vendor specification)

p = Density

= Flow Velocity


Pressure drop by gravity or vertical elevation

  

Where:

= Pressure Drop

p = Density

g = Acceleration of Gravity

= Vertical Elevation or Drop


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:

p1 = Pressure incoming

T1 = Temperature incoming

p2 = Pressure leaving

T2 = Temperature leaving

We set the pipe friction number as a constant and calculate it with the input-data. 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).

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