Water Well Journal
Issue link: http://read.dmtmag.com/i/529509
Centrifugal pumps operate on the same basic principle as the Law of Falling Bodies and the pressure output, or head, is therefore determined largely upon the velocity of the fluid as it exits the impeller. It stands to reason the faster you generate the velocity, the more head is generated as well. It should also make sense when you slow down the velocity of the fluid exiting the impeller, you will have a resultant loss of head. This interrelationship is determined through a set of funda- mental hydraulic principles called the affinity laws. Since the head a pump can generate is largely determined by how fast the outer edge is travelling, then it makes sense this speed can be generated through a large diameter impeller and the periph- eral speed the impeller travels. The affinity laws address this relationship for both the speed component and the impeller diameter component: For pump speed: Q = RPM 1 Head = RPM 1 2 HP = RPM 1 3 RPM 2 RPM 2 RPM 2 For impeller diameter: Q = Dia. 1 Head = Dia. 1 2 HP = Dia. 1 3 Dia. 2 Dia. 2 Dia. 2 As an example, referring back to our original pump curve, this time shown for different speeds (Figure 4), we will use a pump with an original design condition of 650 GPM at 230 feet TDH requiring 47.78 input HP that operates at 2950 RPM (COS #1) with a desired reduction to 2400 RPM (COS #2). The first affinity law states: "The flow of an impeller is directly proportional to a change in speed." When we state "directly proportional," we mean the change in the discharge flow rate is the same or equal to the change in the speed or diameter. This always applies to the speed and basically means if we lower the speed of an im- peller by 20%, the discharge output of that same impeller will also decline by 20%. The same basic relationship holds true for changing the impeller diameter (although there are minor variances with this factor we will discuss in greater detail later). The first affinity law applies as follows: 2400 RPM = (.8136) 1 = .8136 × 650 GPM = 528 GPM 2950 RPM (new operating flow rate) The second affinity law states: "The head of an impeller varies as the square of a change in speed." The law starts to become a little more complex at this point, but simply means the ratio of a change in speed multi- plied by itself and then multiplied by the original head will result in the modified or new head. In this case, assume our original speed of 2950 RPM and a new speed of 2400 RPM once again. The modified head from the change of these two speeds becomes: 2400 RPM/2950 RPM = (.8136) 2 = .8136 × .8136 = .6619 × 230 feet TDH = 152 feet TDH (new operating head) Twitter @WaterWellJournl WWJ July 2015 47 Figure 4. Previous pump curve in Figure 1 modified for different speeds. ENGINEERING continues on page 48