One of the most typical questions asked by process or hydraulic engineers is what is the value of hydraulic resistance (K-factor) of piping component (fitting, valve etc) and how to calculate it for different types of flow? This is one of the most fundamental questions we deal with in PASS/HYDROSYSTEM, and I will be happy to share some knowledge and experience about it. And let’s start from the most simple aspect – K-factor for incompressible liquid.

The most often referenced document for minor pressure losses in the piping is Crane Technical Paper 410 (or simply Crane TP-410). Here you can buy the latest version:


However, it is not the best or most comprehensive source of data on K-Factors! Another much more advanced and respectable world standard is famous “Handbook of Hydraulic Resistance” by Russian Professor I.E. Idelchik. This book became a reference book for generations of piping hydraulic engineers. Please read what Trey Walters, the President of AFT, writes about Professor Idelchik and his book, in his blog: “How a Russian Hydraulics Handbook Gained the Respect of the American Nuclear Industry”.

The latest 4th English edition is available here:

Another worldwide acknowledged and must-have book is “Internal Flow Systems” by famous BHRA researcher D.S. Miller.

This book exists in different editions. We use 2nd edition (from BHR Group), and it is still possible to buy it via Amazon or other online book stores. The latest 3rd edition is mentioned here https://www.mentor.com/products/mechanical/flomaster/don-miller/internal-flow-systems , but we failed to order it (for reasons unclear for us).

So PASS/HYDROSYSTEM basically uses Idelchik K-Factors crossed-checked by Miller data. Moreover, I.E. Idelchik personally checked and tested some correlations for initial version of PASS/HYDROSYSTEM 40 years ago!

But this is only the top of the list of K-factor sources.

Another very useful and important source of information is IHS ESDU documents.

The related ESDU series are the following: – ESDU Fluid Mechanics, Internal Flow Series – ESDU Fluid Mechanics, Internal Flow (Aerospace) Series – ESDU Heat Transfer Series. Many interesting reviews and references are hidden there.

There also are some recent reviews – of which I especially like “PIPE FLOW. A Practical and Comprehensive Guide” by D.C. Rennels and H.M.Hudson”.

Calculation of K-factors of T-junctions is one of the most complex topics, as their values depend on 1) ratio of run and side branch flow rates 2) ratio of side and run diameters 3) type of T-junctions (different variants of combining and dividing).

This subject was studied for almost a century, and still there are holes! I will only consider 90 degree tees here and will give the most important references. Besides Idelchik and Miller (which give good review on this – but not free from errors!) and 2 ESDU documents (ESDU 73022 and ESDU 73023), there are several classical experimental research works which we (and other specialist) use. Below are some most important of them.

First of all, classical articles by A. Gardel:

Another classical works are articles by Hidesato Ito and his colleagues:

And in the beginning of this century, two students of Dr. Ahmet Selamet from the Ohio State University – Adam Christian and Jacques Paul – and other members of his research team made very good experimental work and filled some “holes” for symmetrical combining and dividing T-junctions:

Of course, this is only the top of the iceberg! Minor losses for non-circular pipes, for compressible flow and multiphase flow are another huge topics. And there are still lots of holes in our knowledge… But more about this and other topics in future articles!

So please join us in our journey for dark and secret places and hidden treasures of piping hydraulics!

PASS/HYDROSYSTEM is piping network fluid flow analysis software and a part of PASS software suite for piping stress analysis, hydraulics and thermal analysis, boiler & pressure vessel, heat exchanger, column, tank design & stress analysis is available worldwide since 2018.
About the Author: Leonid Korelstein (LinkedIn) – VP on R&D of PSRE Co (LinkedIn), and one of the leaders of PASS Suite (LinkedIn, Facebook) team. He is also the Product Manager of PASS/HYDROSYSTEM (LinkedIn group), PASS/RELIEF and PASS/INSULATION software. Leonid has PhD in Mechanics and Mathematics, and is Associate Professor (for Chemical Plant design and simulation software) in Mendeleev Chemical University, member of AIChE, active participant of DIERS, EDUG and TUFFP research communities, co-author of AIChE CCPS GPREH book and Russian GOST 12.2.085-2017 standard for pressure relieve systems sizing. He is also active member of ASSESS Initiative.

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