Pump Affinity Laws

My guess is that if what you say is true, then the difference is to do with different pump types - in particular the centrifugal and turbine types.

For a turbine the specific speed Ns is

Ns = N root P/ root rho (g H) ^5/4

where as for a pump Ns is

Ns = N root Q / H^3/4

I thing that you did not read carefully the text accompanying the formulae:

Centrifugal pumps with same size (diametres) and same fluid density, the affinity laws talk about the rpm ratios to the capacity, power required, and pressure developped to have respectively ^1, ^2, ^3 factors.

Same pumps but with constant speed and same fluid density, you now replace the speed ratio with the Diametres ratio and have your set of formulae with ^3, ^2 & 5 factors.

(I have avoided to re-write the formulae but think i was clear)

Dear LAA Lucke,

I think that TrevorM gave the best answer. He direct us to the same discussion held 6 years ago (http://www.eng-tips.com/viewthread.cfm?qid=89032&page=73). There we can see that this is an old confusion. I think that hydrae and Scipio gave excellent answers. It is true that in textbooks they always give the set of expressions with 5th power, and in handbooks with 3rd power. Above gentlmen say that the reason is that textbook talk about complete scaling of whole pumps, which is theretical matter, and handbooks, which are more practical, talk about scaling impeller in one and same housing - which is common thing in tuning a pump. Experience has shown that for impeller scaling the set of expressions with 3rd power is more suitable.

Dear Ingeniarius,

You are right about the topic being correctly handled by TrevorM.

As we can see, the topic is a hard one to come to a 100% correct response to the OP question. He will still be confused on what to do after reading all of these.

What he needs to understand is that there are theoretical guidance but in practice, there is a lot of variables to handle. The best way to do is to go step by step, with small trimmings at a time (if at all this is what he is trying to do!!), and check the performance to see if what he is aiming at is being reached.

If on the other hand he is looking at the issue from an accademic point, then he got a lot of info and I intended to give what was in the text books.

In some manufacturers HandBooks, they even give ^2, ^2, ^3 respectively for Flow, Pressure and Power equations. Well if it was me, I would Take ^2, ^3 & ^4 for the Diametres Trimming equations, considering that the Thickness of the impeller does not change etc... Maybe some one involved in pumps in a more professional way and has had some data in performing small trimming can examine this set and let me know how it fares. (I work it out. Not just a guess.).

Thanks

Further to my earlier comment and a little more checking. It seems that both sets of laws are used, the first for small changes in diameter of a geometrically similar impeller and the second for larger changes.

There is an extended discussion at http://www.eng-tips.com/viewthread.cfm?qid=89032&page=73, which seems well informed.