Equivalent Pipe Length Method

Equivalent Length Method

The equivalent length method (The Le/D method) allows the user to describe the pressure loss through an elbow or a fitting as a length of straight pipe.

This method is based on the observation that the major losses are also proportional to the velocity head (v2/2g).

equivalent length method

The Le/D method simply increases the multiplying factor in the Darcy-Weisbach equation (i.e. ƒ.L/D) by a length of straight pipe (i.e. Le) which would give rise to a pressure loss equivalent to the losses in the fittings, hence the name “equivalent length”. The multiplying factor therefore becomes ƒ(L+Le)/D and the equation for calculation of pressure loss of the system is therefore:

equivalent lengthAll fittings, elbows, tees,  can be summed up to make one total length, and the pressure loss calculated from this length. It has been found experimentally that if the equivalent lengths for a range of sizes of a given type of fitting are divided by the diameters of the fittings then an almost constant ratio (i.e. Le/D) is obtained. The advantage of the equivalent length method is that a single data value is sufficient to cover all sizes of that fitting and therefore the tabulation of equivalent length data is relatively easy. Some typical equivalent lengths are shown in the table.

See also: Pipe Sizing and Flow Calculation Software

table of equivalent lengths - valves, elbows, bends

Summary:

  • Head loss of hydraulic system is divided into two main categories:
  • A special form of Darcy’s equation can be used to calculate minor losses.
  • The minor losses are roughly proportional to the square of the flow rate and therefore they can be easy integrated into the Darcy-Weisbach equation through resistance coefficient K.
  • As a local pressure loss fluid acceleration in a heated channel can be also considered.

There are following methods:

  • Equivalent length method
  • K-method (resistance coeff. method)
  • 2K-method
  • 3K-method

Why the head loss is very important?

As can be seen from the picture, the head loss is forms key characteristic of any hydraulic system. In systems, in which some certain flowrate must be maintained (e.g. to provide sufficient cooling or heat transfer from a reactor core), the equilibrium of the head loss and the head added by a pump determines the flowrate through the system.

Q-H characteristic diagram of centrifugal pump and of pipeline
Q-H characteristic diagram of centrifugal pump and of pipeline
 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.
  10. White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417

See above:

Minor Loss