Talk:Affinity laws

Affinity Law
in support of the comments raised below for a centrifugal pump (or fan) the velocity of the fluid exiting the impeller is proportional to Diameter, whereas the flow (assuming geometrically similar impellers) is proportional to the cube of diameter, as not only the flow velocity increases but the flow passage in the impeller has increased in proportion to the square of the diameter increase hence:

Q1/Q2 = N1/N2*D1^3/D2^3 meaning the wiki article is factually wrong in presenting:

Q1/Q2 = N1/N2*D1/D2

This is stated in any good text on the subject and needs corrected as anyone using the formula presented could make some really bad mistakes in selecting a pump size  — Preceding unsigned comment added by 90.255.214.32 (talk) 12:48, 11 June 2020 (UTC)

Affinity Law Reference
Hi There,

I Apologize in advance for the formatting and posting mistakes made here. I have no idea how this site works but I also picked up the issue regarding to the relationship between head, flow and power to diameter. I would like to offer my 2nd year fluid mechanics textbook Fluid Mechanics (J. Douglas, M.Gasiorek & J.Swaffield) as a reference to support what this relationship should be. Q ∝ N*D^3              (equation 23.27) gH ∝ N*D^2             (equation 23.28) P ∝ ρ*N^3*D^5          (equation 23.29) Where Q = Flow H = Height height P = Power g = Gravitational acceleration constant ρ = Density N = Speed D = Machine wheel diameter Would love to re-open this discussion because. Many people use the internet to quickly check engineering equations. These pump affinity laws are used too frequently and a mistakes could be very costly in real world applications. Braam Daniels (talk) 07:44, 18 February 2018 (UTC)

Comments
I suggest Any comments? Chrike 16:21, 24 October 2007 (UTC)
 * 1) nondimensionalize the variables, e.g. replace rpm with speed N, replace cfm with volumetric flowrate V dot
 * 2) make sure that it is clear that the affinity laws assume the pump efficiencies remain constant and the system performance curve also remains constant. In addition, they don't apply as well to open-loop geodetic situations.
 * 3) add the rest of the affinity laws, such as changing the diameter of the pump blades

There is an article about fan characterictics on german wiki de:Ventilatorkennlinie. Maybe someone can use it to extend this article.--Green3cats (talk) 16:45, 7 November 2008 (UTC)

Application to pumps
I am not sure that the affinity laws apply to all pump types. The literature confirms that they apply to all types of Centrifugal pumps, including radial, mixed flow and axial flow pumps. --GILDog (talk) 12:34, 21 June 2009 (UTC)

"The affinity law for a centrifugal pump with the speed held constant and the impeller diameter changed" are different than stated in the wikipedia. Kindly refer following link for correct formulas.

http://www.pumpworld.com/Affinity%20Laws.htm

-  Shinde Vijaysingh M.Tech. IIT Kanpur

The laws as stated on the main page are designed for shaving off the impeller, and do not satisfy the assumption of dynamic similitude. The mathematically correct version is:
 * $$ { Q \over {N^2 D^3}} = constant  $$     and     $$ { h \over {N^2 D^2}} = constant   $$

However, I now realise that the version on the main page is more accurate for changing the impeller diameter without altering any other pump dimensions (e.g. the volute)--GILDog (talk) 11:41, 29 April 2010 (UTC)

I believe the formula for the diameter changes are wrong. For axial fans the indices are 3 for flow, 2 for pressure and 5 for power. I don't want to change it as it may be different for other kinds of fluid moving devices (but I doubt it). 62.189.28.130 (talk) 09:08, 25 March 2011 (UTC)

D not diamater
Indication on Swedish side (Affinitetslagarna) that D is actually not the impeller/fan diameter, but more of a "size". No refererence though. — Preceding unsigned comment added by WikyHicky (talk • contribs) 14:27, 9 June 2011 (UTC)

Proportionality of power and impeller diameter
There seem to be two camps: Some say Power is proportional to the cube of the diameter and some say it's proportional to the fifth power of the diameter. In the history of this article, this has been changed several times. When googling for other sources, no improvement :( Is there any source for ^3 vs ^5? What are the assumptions? I consulted several books about fan design, but didn't find any affinity relations for the fan diameter. ^3 seems plausible as Pressure*Flow is equal to Power, ^5 might come from pressure drop in duct resistances? Kelaodisi (talk) 14:57, 17 January 2012 (UTC)

The power coefficient derived by dimensional analysis for a centrifugal pump is in the form $$\textstyle C_p = \frac{P}{\rho n^3 D^5} $$, where $$\textstyle\rho$$ is the density, n is the pump speed and D is the pump diameter. Keeping $$\textstyle\rho$$ and n constant and equating $$\textstyle C_{p1} = C_{p2}$$ we get $$\textstyle\frac{P_1}{P_2} = (\frac{D_1}{D_2})^5$$. --RicardoHM (talk) 17:27, 17 January 2012 (UTC)

according to http://www.engineeringtoolbox.com/affinity-laws-d_408.html $$Q1/Q0=D1/D0$$ for diameter change of identical pumps, $$Q1/Q0=(D1/D0)^3$$ for diameter change of geometrically similar pumps! this doesnt really make sense to me as surely a diameter change negates it being identical and even if it was then why arent two "identical" pumps geometrically similar? Also on the same website they say that the affinity laws for FANS are different to PUMPS but the fan affinity law is just $$Q1/Q0=(D1/D0)^3$$. In the other two references http://www.pumpfundamentals.com/yahoo/affinity_laws.pdf and http://www.airturbine.com/fanlaws.html they only give $$Q1/Q0=(D1/D0)^3$$. Also I think the Power law just comes from multiplying the pressure and flow equations together which is why you get the exponent of five for the power when the flow is cubic. [hugh hopper] 1355 28th June 2013 — Preceding unsigned comment added by 62.189.28.130 (talk) 12:56, 28 June 2013 (UTC)

I just want to point out that the hyperlink reference to support Law 2 does not match what is written with respect to law 2a and 2c. I can cite some pages from an old pump handbook that seem to clarify this, but I don't know how to

http://www.engineeringtoolbox.com/affinity-laws-d_408.html — Preceding unsigned comment added by 147.182.5.150 (talk) 14:30, 19 December 2013 (UTC)

The so-called "Affinity Laws" apply only to turbo-machinery, and then only to turbo-machinery having identical geometry for impeller and housing. The "Affinity Laws" are derived from similarity considerations. For example, volumetric flow rate(Q) has dimensions of length (L) cubed and time (T) to raised to the power -1: [Q] = [L]^3 [T]^-1. Shaft speed has dimensions [T]^-1. Diameter has dimension [L]. Putting the parts together yields Q = k1 N D^3, where D is a dimension characteristic of the turbo-machine, such as the impeller diameter, and N is the rotational speed of the machine expressed in revolutions/second, say. k1 is a constant of proportionality. The requirement that different sized pumps be geometrically similar (i.e., differences in scale are permitted, but differences in shape are not) arises because D is a representational dimension only -- all other dimensions scale proportionately to D. To illustrate, if the housing size D1 is changed but the impeller diameter D is not changed, the "Affinity Laws" will not apply. The relationships for developed head (H) and hydraulic power (P) are likewise derived from dimensional considerations. Head (H) is measured in metres (m), or more correctly in units of [L]^2 [T]^-2 as gH, g is the gravitational acceleration (9.81 m/s/s). Thus, gH = k2 N Q^1.5 = k2 N^2 D^2, where k2 is a constant of proportionality. Power (P) is measured in watts (or lbf-ft/sec) or in fundamental units [M][L]^2[T}^-3. Thus, Power = Head (gH) x Volumetric Flow Rate (Q), and we can write the similarity relation for power as P = k3 N^2 D^2 N D^3 = k3 N^3 D^5, where the fluid density is taken into the constant of proportionality, k3. To sum up, the so-called "Affinity Laws" arise from a dimensional analysis and depend on similarity of flow regime in geometrically similar turbo-machinery. The relations demonstrated in the forgoing discussion are: Flow rate, Q = k1 N D^3 Flow head, gH = k2 N^2 D^2 Hydraulic power, P = k3 N^3 D^5.

The "Affinity Laws" follow directly from the dimensional analysis by forming the ratios: Q1/Q0, H1/H0, and P1/P0, provided the machines 1 and 0 are geometrically similar, and, in the case of the power ratio that the fluid densities are also identical. — Preceding unsigned comment added by Súl iolar d'aois (talk • contribs) 16:23, 29 April 2014 (UTC)

Affinity Law update
I have noticed that despite multiple contributors on the talk page and appropriate references and engineering analysis demonstrating the case that the Affinity laws have been again adjusted to the wrong values in relation to geometrically similar pump and scaling with pump diameter. Again this could lead to large errors the correct power laws are stated in the talk but the article is factually wrong 217.33.165.88 (talk) 13:37, 20 December 2023 (UTC)