Pump affinity laws

[Ingeniarius]

Dear colleagues,
why do we find two different sets of pump affinity laws in literature and on the web:
One set is correct (according to my knowledge) and says that for constant shaft speed the following is true Q1/Q2=D1^3/D2^3, H1/H2=D1^2/D2^2 and P1/P2=D1^5/D2^5.
The other set of laws that is widespread on the net (almost exclusive) and even in literature says that Q1/Q2=D1/D2, H1/H2=D1^2/D2^2 and P1/P2=D1^3/D2^3.
What is true, and how is it possible that in engineering community agreement is not reached regarding the most fundamental laws of practical hydrodynamics.
Best regards!

 

[BigInch]

Perhaps you are a little confused about the equipment,

FANS

http://www.engineeringtoolbox.com/fan-affinity-laws-d_196.html

PUMPS

http://www.engineeringtoolbox.com/fan-affinity-laws-d_196.html

"We have a leadership style that is too directive and doesn't listen sufficiently well. The top of the organisation doesn't listen sufficiently to what the bottom is saying." Tony Hayward CEO, BP

**********************
"Being GREEN isn't easy" ..Kermit

http://www.youtube.com/watch?v=hpiIWMWWVco

http://vir

 

[ScottyUK]

BigInch's second link should of course be

http://www.engineeringtoolbox.com/affinity-laws-d_408.html

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If we learn from our mistakes I'm getting a great education!

 

[25362]

The first set of equations refers to a comparison between different centrifugal pumps with geometrically similar impellers, operating with identical specific speeds. Model laws are only applicable at constant efficiency.

The second set refers to the same pump. These equalities are not as accurate as the laws relating to rpm denoted by n:

Q [ε] n; H [ε] n²; P [ε] n³ and NPSH [ε] n²​

Sulzer, in its Centrifugal Pump Handbook (Elsevier), says that when reducing radial impeller diameters on a single pump:

Q₂/Q₁ = (D₂/D₁)^m and H₂/H₁ = (D₂/D₁)^m​

m = 2 for corrections [≥] 6%
m = 3 for corrections [≤] 1%

 

[BigInch]

Hummm. Makes me wonder when a 1% change really worth making.

"We have a leadership style that is too directive and doesn't listen sufficiently well. The top of the organisation doesn't listen sufficiently to what the bottom is saying." Tony Hayward CEO, BP

**********************
"Being GREEN isn't easy" ..Kermit

http://www.youtube.com/watch?v=hpiIWMWWVco

http://vir

 

[Artisi]

Agreed, unless you are talking VERY large units a 1% change isn't even worth a consideration.

 

[25362]

I've written in bold letters radial impellers. I'm no pump expert, I was only a user and am still a reader. In the Pump Handbook by Karassik et al., McGraw-Hill, when referring to radial vanes, we find, among other statements:

...Radial vane pumps are used in many applications, from cellar drainers, cooling water pumps for internal combustion engines, and other applications where low first cost is more important than high efficiency to highly engineered pumps designed for very high heads. The impellers are rarely more than 6 in (15 cm) in diameter, but the speed range may be from a few hundred to 30,000 rpm or more....
Such pumps exhibit a flat head-capacity curve from shutoff to approximately 75% of best efficiency capacity, and beyond this flow the head-capacity curve is steep. The pumps develop a higher head, up to 8000 ft (2400 m) per stage, than pumps with backward-curved vanes, but the efficiency of the former usually is lower.

 

[dabluffrat]

It's worth noting Johnston Pump, now Sulzer, has adopted another trim calc for vertical pump impellers Ns > 1000.

Vertical Turbine, Mixed Flow, & Propeller Pumps by John L. Dicmas

"Analysis of a large number of turbine pump impellers in the specific speed range from 1500 to 6000 indicates that while theoretical capacity and head exponents are 1 and 2, respectively, this applies to radial impellers only, and both exponents increase as a function of specific speed."

Figure 2.20 goes on to show the exponent relationship as a function of Ns based on years of compiled test data.

Did you know that 76.4% of all statistics are made up...

 

[Yobbo]

Wasn't it Mr. Karassik, who presented a formula for the dependance of the pump efficiency on the speed of the pumprotor? The dependancy is (n/nbep)^0.1. The affinity laws are based on the assumption that the efficiency remains constant, while the pumpspeed changes. I wonder in what ways Karassik's formula changes that.