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Formulae for calculating pipe pressure drops

Formulae for calculating pipe pressure drops

Formulae for calculating pipe pressure drops


When calculating the pressure drops in steam pipes, does anyone know whether it is best to use the Fritzsche or Darcy equation or if one formula is more accurate than the other in some ranges of pressure and temperature.

Best regards


RE: Formulae for calculating pipe pressure drops

The Fritzche's equation is always better because it takes into account the compressibility of the steam gas.

This book is a good source...

ISBN 007 144090 9

RE: Formulae for calculating pipe pressure drops

Darcy's equation is derived from Bernoulli's equation and it has the main limitation of incompressibility of fluids that are dealt, as suggested by yedwa. At very low pressures (with static pressure of few inches of WC), you can use Darcy's. Crane TP410 gives you couple of methods.

RE: Formulae for calculating pipe pressure drops

Darcy's equation is the equation of choice for incompressible fluids.  Nevertheless, it can be used to accurately predict pressure drops in compressible fluids, such as air, steam, etc.  The following restrictions should be observed in applying the Darcy equation:

1. Because of the basis of isothermal flow (constant density), if the calculated pressure drop is less than about 10% of the inlet pressure, reasonable accuracy will be obtained if the specific volume used in the formula is based upon either the upstream or downstream condtions, whichever are known.

2. If the calculated pressure drop is greater than about 10%, but less than about 40% of inlet pressure, the Darcy equation may still be used with reasonable accuracy by using a specific volume based upon the average of upstream and downstream conditions.  Otherwise, the "Modified" Darcy formula (which includes the "Y" compressibility factor) is to be used.

3. For greater pressure drops (>40% of inlet pressure), such as are often encountered in long pipe lines, the methods detailed out in Crane's Technical Paper #410 should be employed.  This includes the "Modified" Darcy equation.

The Panhandle equations, Fritsche's, Weymouth's, etc. are all empirical variations and attempts to define compressible flow.  All these equations have their trade-offs and their flaws, as well as inaccuracies.   There is no known "super" or compressible equation for all seasons.

Unless you have a bias against using Crane's Tech Paper #410, I would go with what quark suggests: use Crane.  Crane even gives you specific examples of how to do the calculations with steam as the fluid.  I do not believe that the modified Darcy equation is limited to very low pressures.  Crane does not mention this nor do the examples calculations they offer.

RE: Formulae for calculating pipe pressure drops


Thank you for your advice. I do not have any bias against using Crane 410, in fact it is my preferred method.

I am checking some pressure drop calculations for four systems operating at different pressures. The pipe supplier is using the average of the pressure drops calculated by both the Darcy and Fritzsche formulae for the 105bar system and the Fritzsche formula for the 45, 20 and 5 bar systems claiming that this gives pressure drops higher than their experience.

The reason for my question was to seek the experience and opnions of others.

I have reservations about the Fritzsche formula because I do not understand the derivation and find it difficult to accept that a formula that does not include the friction factor can be acurate over a wide range of Reynolds numbers.

yedwa - can you advise the title of the book?

Best regards,


RE: Formulae for calculating pipe pressure drops

The title of the book is
: piping calculations manual by E shashi menon.

very good book.

RE: Formulae for calculating pipe pressure drops


Your experience with the Fritzsche equation is precisely the reason I have been advising all engineers working with me, under me, and on this forum: do not employ any equation you read about or receive from others unless you have full documentation and identification - or can derive it yourself.  For my personal calculations, I don't use an equation that I personally can't derive or back up with accepted and recognized documentation.

Fritzsche's equation is valid (with limited accuracy) for those empirical applications from which it was derived.  If the applications can't be identified, the accuracy has to be challenged.  No other equation has been put to the test as has Darcy's relationship.  The field data is there, the experience factor is there, and the applications are there.  That's why it is the equation of choice.  Even in compressible flow, I have subdivided the piping segments into 7-10 psi increments and resolved the pressure drop with accurate predicitions - just as Crane suggests.

In my opinion you are doing the correct, engineering decision in challenging an equation that doesn't identify the basic friction resistance value or source while presumably calculating a pressure drop within a piped system.  You have every right to demand the basic data as well as the basic premise for an alleged solution to the problem.

RE: Formulae for calculating pipe pressure drops

Thank you Gentlemen,

Montemayor, I follow the same philosophy as yourself.

Thanks again


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