ASHRAE Journal - March 2011 - 42

U

By Richard W. Ford, Member ASHRAE

Affinity Laws
nderstanding the affinity laws and why they work is key in applying the laws correctly. A common first impression is that

Why They Work & When They Don’t

Aff inity Laws

“centrifugal pumps are more efficient at lower speeds.” This is incorrect. One journal recently published the statement: “You can

•	 Flow is proportional to the speed of a pump. •	 Pressure output is proportional to the square of the speed. •	 Power needed is proportional to the cube of the speed.

run two pumps at half speed for less power than it takes for one work. We see that force to overcome pump at full speed.” The author thought that pump efficiency was the flow rate and distance is analogous proportional to the cube of the speed; therefore, you could pump to the flow rate. The flow times the the same amount of water with one-fourth of the power.
Actually, the affinity laws do not make any statement about efficiency of the pump. In fact, the laws predict accurate results only when there will be no change in pump efficiency. To understand what the laws do predict, let’s back up to a law we learned in high school physics: Work = Force × Distance To relate “distance” to a pump application, imagine a long, horizontal pipe with a cross-sectional area of one square foot (or one square meter). The distance that the liquid moves through the pipe equals the flow in cubic feet (cubic meters). Any flow through a pipe must overcome the force of friction. The Darcy-Weisbach equation for pressure drop in a pipe is: Dp = f (L/D)(r/gc)(V 2/2) where p = pressure; f = friction factor; L = length of the pipe; D = diameter; r = density; and V = velocity.
42 ASHRAE Journal

Now look back at the definition of

friction is proportional to the square of

Focus on the fact that the equation that shows that pressure drop is proportional to the square of the velocity. McAdams1 uses a formula for pressure drop that shows the effect of both the force of friction and the force of gravity: p1 – p2 = z2 – z1 fm G 2 vm L g +g × v 2gc rh c m

where G = mass velocity of fluid (weight/second divided by the crosssectional area, or lb/s·ft2); fm = mean friction factor; p = pressure; vm = mean specific volume; L = length of the pipe; rh = hydraulic radius; and z = height. The left term defines the force needed to overcome friction, while the right term defines the force needed to overcome gravity. The right term does not have any variable related to velocity. The force of gravity stays the same, whether you pump water up hill fast or slowly.
ashrae.org

square of the flow is the cube of the flow. That’s all the cube law tells us; the work to overcome friction is proportional to the cube of the flow rate. The work that the pump must do to overcome friction is proportional to the cube of the flow rate no matter what means you use to vary the flow rate. You can install a variable speed drive or install a smaller impeller. There will be a change in pump efficiency if you change to a smaller impeller, but you always come out with some savings. The pump manufacturer will have a different pump curve for every size of impeller (Figure 1). A variable speed drive usually will do a better job of maintaining pump efficiency, but capital costs may be lower for cutting the size of the impeller. Look carefully at any pumping system curve. Does that shape look familiar from your college analytical geometry class? The parabolic shape is characteristic of a y-value that is proportional to the

About the Author
Richard W. Ford is an energy engineer in East Amherst, N.Y.

March 2011



ASHRAE Journal - March 2011

Table of Contents for the Digital Edition of ASHRAE Journal - March 2011

ASHRAE Journal - March 2011
Contents
Commentary
Industry News
Meetings and Shows
Feature Articles
ASHRAE’s Best: 2011 Technology Awards
Technology Award Case Studies: Hospital Retrofit
Energy Savings for Quick Service Restaurants
Affinity Laws: Why They Work & When They Don’t
Data Center Heat Rejection: Indirect Air-Side Economizer Cycle
Health Care Standard Update
Building Sciences
Solar NZEB Project
HVAC Mythbuster
Washington Report
Emerging Technologies
IAQ Applications
Special Products
People
Classified Advertising
Advertisers Index
ASHRAE Journal - March 2011 - Intro
ASHRAE Journal - March 2011 - ASHRAE Journal - March 2011
ASHRAE Journal - March 2011 - Cover2
ASHRAE Journal - March 2011 - 1
ASHRAE Journal - March 2011 - 2
ASHRAE Journal - March 2011 - Contents
ASHRAE Journal - March 2011 - Commentary
ASHRAE Journal - March 2011 - 5
ASHRAE Journal - March 2011 - Industry News
ASHRAE Journal - March 2011 - 7
ASHRAE Journal - March 2011 - 8
ASHRAE Journal - March 2011 - 9
ASHRAE Journal - March 2011 - 10
ASHRAE Journal - March 2011 - 11
ASHRAE Journal - March 2011 - 12
ASHRAE Journal - March 2011 - 13
ASHRAE Journal - March 2011 - 14
ASHRAE Journal - March 2011 - 15
ASHRAE Journal - March 2011 - 16
ASHRAE Journal - March 2011 - 17
ASHRAE Journal - March 2011 - 18
ASHRAE Journal - March 2011 - 19
ASHRAE Journal - March 2011 - Meetings and Shows
ASHRAE Journal - March 2011 - 21
ASHRAE Journal - March 2011 - ASHRAE’s Best: 2011 Technology Awards
ASHRAE Journal - March 2011 - 23
ASHRAE Journal - March 2011 - 24
ASHRAE Journal - March 2011 - 25
ASHRAE Journal - March 2011 - 26
ASHRAE Journal - March 2011 - 27
ASHRAE Journal - March 2011 - 28
ASHRAE Journal - March 2011 - 29
ASHRAE Journal - March 2011 - 30
ASHRAE Journal - March 2011 - 31
ASHRAE Journal - March 2011 - Technology Award Case Studies: Hospital Retrofit
ASHRAE Journal - March 2011 - 33
ASHRAE Journal - March 2011 - 34
ASHRAE Journal - March 2011 - 35
ASHRAE Journal - March 2011 - Energy Savings for Quick Service Restaurants
ASHRAE Journal - March 2011 - 37
ASHRAE Journal - March 2011 - 38
ASHRAE Journal - March 2011 - 39
ASHRAE Journal - March 2011 - 40
ASHRAE Journal - March 2011 - 41
ASHRAE Journal - March 2011 - Affinity Laws: Why They Work & When They Don’t
ASHRAE Journal - March 2011 - 43
ASHRAE Journal - March 2011 - Data Center Heat Rejection: Indirect Air-Side Economizer Cycle
ASHRAE Journal - March 2011 - 45
ASHRAE Journal - March 2011 - 46
ASHRAE Journal - March 2011 - 47
ASHRAE Journal - March 2011 - 48
ASHRAE Journal - March 2011 - 49
ASHRAE Journal - March 2011 - 50
ASHRAE Journal - March 2011 - 51
ASHRAE Journal - March 2011 - 52
ASHRAE Journal - March 2011 - 53
ASHRAE Journal - March 2011 - 54
ASHRAE Journal - March 2011 - 55
ASHRAE Journal - March 2011 - Health Care Standard Update
ASHRAE Journal - March 2011 - 57
ASHRAE Journal - March 2011 - 58
ASHRAE Journal - March 2011 - 59
ASHRAE Journal - March 2011 - 60
ASHRAE Journal - March 2011 - 61
ASHRAE Journal - March 2011 - Building Sciences
ASHRAE Journal - March 2011 - 63
ASHRAE Journal - March 2011 - 64
ASHRAE Journal - March 2011 - 65
ASHRAE Journal - March 2011 - 66
ASHRAE Journal - March 2011 - 67
ASHRAE Journal - March 2011 - 68
ASHRAE Journal - March 2011 - 69
ASHRAE Journal - March 2011 - Solar NZEB Project
ASHRAE Journal - March 2011 - 71
ASHRAE Journal - March 2011 - 72
ASHRAE Journal - March 2011 - 73
ASHRAE Journal - March 2011 - 74
ASHRAE Journal - March 2011 - 75
ASHRAE Journal - March 2011 - 76
ASHRAE Journal - March 2011 - 77
ASHRAE Journal - March 2011 - HVAC Mythbuster
ASHRAE Journal - March 2011 - 79
ASHRAE Journal - March 2011 - Washington Report
ASHRAE Journal - March 2011 - 81
ASHRAE Journal - March 2011 - Emerging Technologies
ASHRAE Journal - March 2011 - 83
ASHRAE Journal - March 2011 - 84
ASHRAE Journal - March 2011 - 85
ASHRAE Journal - March 2011 - IAQ Applications
ASHRAE Journal - March 2011 - 87
ASHRAE Journal - March 2011 - 88
ASHRAE Journal - March 2011 - 89
ASHRAE Journal - March 2011 - Special Products
ASHRAE Journal - March 2011 - People
ASHRAE Journal - March 2011 - 92
ASHRAE Journal - March 2011 - 93
ASHRAE Journal - March 2011 - 94
ASHRAE Journal - March 2011 - 95
ASHRAE Journal - March 2011 - 96
ASHRAE Journal - March 2011 - 97
ASHRAE Journal - March 2011 - 98
ASHRAE Journal - March 2011 - 99
ASHRAE Journal - March 2011 - 100
ASHRAE Journal - March 2011 - 101
ASHRAE Journal - March 2011 - Classified Advertising
ASHRAE Journal - March 2011 - 103
ASHRAE Journal - March 2011 - Advertisers Index
ASHRAE Journal - March 2011 - Cover3
ASHRAE Journal - March 2011 - Cover4
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