Thank you
You took me dancing
'Cross the floor ... cheek to cheek
But with a lover
I could really move, really move
I could really dance, really dance

("Love and Affection," by Joan Armatrading, 1976)

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order just learned that Centrifugal Pumps are selected for service based upon their chart of Performance Curves.

Quickie review:

• The TDH curve (aka the pump's Characteristic Curve) shows how much Total Dynamic Head can be generated at each point of Capacity.
• The Brake Horsepower Curve indicates the required BHP that will attain the TDH at the pump's Capacity.
• The Efficiency Curve is the curve used to begin pump performance analysis with because it shows where the pump can be operated with maximum Efficiency.

Here's some new information about Performance Curves and Centrifugal Pumps:

Each Performance Curve will specify either:

• The diameter of the spinning Impeller (when the pump has a constant speed driver).
• The speed in revs-per-minute that the Impeller is being rotated (when the pump has a  Variable Speed Driver).

Gee ...

What the heck happens after the purchased Centrifugal Pump is installed and then found to be incapable of generating the actual TDH that is required in the real processing world application?

Fortunately there are several ways to improve Centrifugal Pump performance so that the purchased and installed pump can work well in the real world. Two of the methods are:

• Change the diameter of the Impeller if the driver is a constant speed driver.
• Change the speed of the rotating Impeller if the driver is a Variable Speed Driver.

This PTOA Segment #169 features the impact that changing the size of an Impeller has on Centrifugal Pump Performance.

The next PTOA Segment will feature the impact that changing the speed of the Impeller has on Centrifugal Pump Performance.

In either case, the adjusted performance of the Centrifugal Pump is easy to predict from the original Performance Curve that is supplied by the pump's manufacturer because ...

The Affinity Laws are used to generate parallel Capacity, TDH, and Brake Horsepower Performance Curves.

The Performance Curves that are generated from Affinity Laws represent "stepping up" or "stepping down" the pump's performance.

Do Process Operators need to memorize The Affinity Laws by heart to do a good job?

Heck No!

Process Operators won't ever directly use The Affinity Laws!

However, Process Operators who have been exposed to The Affinity Laws will have a better understanding of the challenges Mechanics have with respect to getting a new pump to optimally operate.

Because efficient pump operation translates into less pump failure and less downtime ...

all Process Operators benefit from understanding how a pump's performance is optimized!

 

THE IMPACT OF CHANGING A PUMP'S IMPELLER
ON CAPACITY AND TDH

The nearby graphic shows the TDH Performance Curves for three Impellers with the following diameters:

• 12.75 inch
• 12.0 inch
• 11.0 inch

 

Affinity Law #1: The Impact of Impeller Size on Capacity

The family of Performance Curves shown above could be generated from any one of the curves using Affinity Laws #1 and #2.

Affinity Law #1 is:

The Capacity varies directly with the diameter of the Impeller.

Sounds fancy. What does that mean?

Well, let's focus on the TDH-Capacity curve for the 12 inch Impeller ... that is the curve in the middle.

Check it out and verify that:

At Capacity=2400 gpm, the TDH=2000 feet.

The Capacity that will be achieved with a longer (or shorter) Impeller can be determined by the following expression:

Capacity with 12.75 inch Impeller = 2400 gpm * (12.75 in/12.0 in)

   = 2400 (12.75/12.0) = 2550 gpm

In other words,

"Stepping up" the performance of the Centrifugal Pump by substituting a 12.75 in Impeller for the 12.0 inch Impeller will increase the Capacity from 2400 gpm to 2550 gpm.

Wow! Is that all there is to it?

The above example shows that the procedure to determine the Capacity for a different size Impeller is:

Just multiply the "old" or "known" Capacity by the ratio of the "new"/"old" Impeller diameters!

 

Affinity Law #2: The Impact of Impeller Size on TDH

Affinity Law #2 can be used to determine the TDH that will be generated when the pump is "stepped up" by substituting a 12.75 inch Impeller for the original 12.0 inch Impeller.

Affinity Law #2:

The TDH varies directly with THE SQUARE of the diameter of the Impeller.

More fancy talk. Translation, please!

This is what Affinity Law #2 means:

First ...

Remember that the middle curve on the nearby diagram showed that a TDH created with the 12 inch Impeller is 2000 feet when the Capacity is 2400 gpm.

Ergo...

 

To determine the TDH generated with a 12.75 inch Impeller, multiply the "old" or "known" TDH by the squared ratio of the (New Impeller Diameter)² / ("Old" Impeller Diameter)² like this:

TDH with 12.75 inch Impeller = 2000 feet (12.75 in)² / (12.0 in)²

 = 2000 * (12.75)² / (12.0)² = 2258 Feet

Voila!

"Stepping up" the pump by replacing the 12.0 Inch Impeller with a 12.75 inch Impeller will create an increased TDH of 2258 feet at an increased Capacity of 2550 gpm.

By selecting a few more points on the 12.0 Inch Impeller TDH-Capacity Curve (aka Characteristic Curve), the Affinity Laws #1 and #2 can be used to predict the entire 12.75 inch Impeller Characteristic Curve.

Likewise ...

The expected outcome of "stepping down" the performance of a Centrifugal Pump by replacing the 12.0 inch Impeller with a shorter, 11.0 inch Impeller can be predicted via The Affinity Laws.

Remember that at the "old" or "known" Capacity of 2400 gpm, a 12.0 inch Impeller creates a TDH = 2000 feet.

Using Affinity Law #1, the Capacity for a 11.0 inch Impeller can be determined:

Capacity with 11.0 inch Impeller = 2400 gpm * (11.0 in / 12.0 in)

 = (2400) * (11 / 12 ) = 2200 gpm

Using Affinity Law #2, the TDH can be predicted for a 11.0 inch Impeller:

TDH for an 11.0 inch Impeller = 2000 feet (11.0 in)² / (12.0 in)²

  = 2000 (121 / 144) = 1681 feet

Aha!

"Stepping down" the performance of a Centrifugal pump by substituting a 11.0 inch Impeller for a 12.0 inch Impeller will result in generating a 1681 foot TDH at a Capacity of 2200 gpm.

Using a couple more points from the 12.0 inch TDH-Capacity curve, the entire 11.0 inch curve can be fleshed out.

 

THE REAL WORLD APPLICATION REGARDING
CHANGING THE IMPELLER DIAMETER

Why The Impeller Diameter Can't Be Too Long

Increasing the diameter of the Impeller sure seems like an easy fix to increase TDH and Capacity!

So what is the limit on how long the Impeller diameter can be?

PTOA Readers and Students will soon learn the important role that the Volute plays with respect to directing the desired flow of the pumped liquid.

See the two upper most arrows in the nearby graphic?

These two arrows indicate the flow of the pumped fluid is entering the Pump Discharge instead of taking another spin around the Volute.

These two arrows show the pumped fluid clearing the Cutwater of the Pump.

The Cutwater of the Pump is the edge of the Volute interior right where the spinning fluid either flows into the Pump Discharge or makes another revolution around the Volute.

If the diameter of the Impeller is too long, the Impeller will rub against the Cutwater of the Volute.

The second great reason to limit the Impeller diameter is that some Efficiency would be sacrificed with the maximum-most-possible Impeller diameter.

A maximum diameter Impeller will have slightly lower Efficiency than the optimally-sized Impeller because of turbulence that would be created near the Cutwater.

 

 

 

 

 

Why The Impeller Diameter Can't Be Too Short

Brilliant PTOA Readers and Students can easily Imagine the reduction in Efficiency that results if the Impeller is cut down to the minimum diameter!

In that case a greater amount of pumped liquid is circulated around and around instead of entering the Pump Discharge.

The circulating liquid creates its own special brand of undesired turbulence!

 

The Optimally Sized Impeller

The optimally sized Impeller may require physical modifications made by expert pump Mechanics.

The outcomes that result after physically modifying an Impeller are not predictable by The Affinity Laws and are performed by experts only.

The nearby graphic (labelled "Figure 1") shows how the original vanes on an Impeller are trimmed back from the labelled "Original vane thickness" by "underfiling" which results in a significantly thinner vane.

As the nearby graphic labelled "Figure 2" shows, the underfiling modification has made a significant impact on the TDH and Capacity.

The Pump's TDH and Efficiency Curves before underfiling are shown as solid lines.

The Pump's TDH and Efficiency Curves after underfiling are represented as dotted lines.

Comparing the before and after vane underfiling reveals:

The maximum pump Efficiency is slightly greater than the Efficiency that the same pump had before the vanes of its Impeller were filed.

The maximum Efficiency occurs where there is a 20% increase in pump Capacity with absolutely no sacrifice in TDH!

Wow! This pump can efficiently handle 20% more Capacity!

Volute Modifications

Although not an Impeller modification, this is as good a place as any to mention that the Cutwater of the Volute and Pump Discharge may also be modified to improve Centrifugal Pump Performance.The nearby graphic (which is labelled "Figure 3") shows the Cutwater of a Volute.

Warning ... don't become confused! The label in the graphic refers to the Cutwater as "the Casing Tongue."

The darkened area of the Cutwater is the part that is trimmed away by an expert pump specialist.

The modifications to the Cutwater indicate the same favorable impacts that were observed when the  Impeller vanes were underfiled!

The nearby graphic (labelled "Figure 4") compares the performance of the pump before and after modification of the Cutwater.

Solid lines represent pump performance "before Cutwater trimming" and dotted lines represent pump performance "after Cutwater was trimmed."

The impacts of the Cutwater modification on pump performance are:

The maximum pump Efficiency is slightly greater after the Cutwater is trimmed.

The maximum Efficiency occurs where there is a 20% increase in pump Capacity with absolutely no sacrifice in TDH!

Wow! This type of modification to the pump can also improve pump efficiency AND make it possible to handle 20% more Capacity!

 

AFFINITY LAW #3:
HOW IMPELLER DIAMETER IMPACTS BRAKE HORSEPOWER

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order already know exactly what is meant by the phase "Brake Horsepower" because they have read PTOA Segment #168.

Affinity Law #3 states how the Brake Horsepower will change as the Impeller diameter is changed:

The Brake Horsepower of the Pump will vary directly as THE CUBE of the Impeller diameter.

Cubing a number means to raise it to the power of 3 ... one more power than squaring!

Here's an example of how Affinity Law #3 is used to predict the BHP that is required when pump performance is "stepped-up."

PTOA Readers and Students will remember that the 12 inch Impeller shown in the nearby graphic creates a 2000 foot TDH at a Capacity of 2400 gpm.

PTOA Readers and Students must also remember Affinity Laws #1 and #2 were used to determine a 12.75 Impeller creates a 2258 ft TDH when the Capacity is 2550 gpm.

Affinity Law #3 predicts what will happen when the Pump's Performance is "stepped up" by replacing the 12 inch Impeller with a 12.75 inch Impeller:

First, assume the BHP required to generate a 2000 ft TDH at 2400 gpm is 131 hp.

Then:

BHP required for 12.75 inch Impeller = 131 hp (12.75 in)³ / (12.0 in)³

   = 131 * (2072)/(1728) = 157 hp

Aha!

When the 12.75 inch Impeller replaces the 12.0 inch Impeller, the BHP required increases from 131 hp to 157 hp for a TDH = 2558 ft at a Capacity of 2550 gpm.

DIY Exercise:

Do it Yourself and figure out what the BHP required is when an 11 inch Impeller replaces the 12.0 inch Impeller.

PTOA Readers and Students who want to delve into the Affinity Laws further might enjoy using this handy dandy link tool provided by EngineeringToolBox.com.

EngineeringToolBoxPumpAffinityLawCalculator

Access the above link, then look for "Pump Affinity Law Calculator - Changing Wheel Diameter." Enter these numbers sequentially and vertically in the blocks: 2400 gpm, 2000 TDH, 131 HP, 12 in Impeller Diameter (aka "Wheel Diameter"), and finally 11 in Impeller Diameter.

Click "CALCULATE."

The tool will calculate the change in capacity in gpm, TDH in feet, and HP that results when changing the Impeller Diameter from 12 in to 11 in.

 

HOW DOES THE PUMP IMPELLER IMPACT THE PUMP'S EFFICIENCY?

PTOA Readers and Students have already learned that there are limits as to how long or short an Impeller can be.

Because there is a limit to an Impeller's diameter, the impact of changing out an Impeller does not impact the pump's Efficiency that much.

Otherwise stated:

Over the real world ranges of an Impeller's diameter, the Efficiency can be assumed to remain constant.

That means if an optimal Efficiency of 80% for a 12.0 inch Impeller is observed, the Efficiency for a 12.75 inch Impeller or an 11.0 inch Impeller can be assumed to be 80%, too!

Below PTOA Readers and Students will see a real world Combination Performance Curve. Note that ... in the operating range of interest for this pump ... the Efficiency changes from 80% to 83%.

 

REAL WORLD COMBINATION PERFORMANCE CHARTS

Real world Performance Curve charts typically show the predicted pump performance with several Impeller diameters.

The nearby graphic describes the Performance Curves for a 4 BC Pump which spins the Impeller at the constant speed of 1750 rpms ... no matter what the size of the Impeller is.

PTOA Readers and Students should notice that the TDH Curves shown are for Impeller diameters that range from 7.5 to 9.5 inch.

The real world Combined Performance Curves chart cannot represent the Efficiency and Brake Horsepower Curves in the same format that is used for single TDH-Capacity relationship.

The Efficiency at each 'step' is shown in the region of interest as a looping downward curve that looks like the  letter "U."

Each point on each U-shape curve represents the same stated Efficiency.

In the nearby graphic the Efficiency U-shaped curves range from 80% (the largest "U") to 83% (the smallest "U" that sort of looks like a "V").

There are other lines of Efficiency that do not make a complete U. For example there are lines of Efficiency marked "75%" and even "60%." These lines are for informational purpose only; in the real world the pump would not be selected to operate everyday in this region.

Note that Brake Horsepower is shown as dashed lines that slant downward and to the right.

Each point on the separate slanted lines represents the same stated HP ... which appears on the right side of the slanted lines.

The labels at the right side of the slanted lines indicate the range of BHP to be 7 ¹/₂ (bottom-most BHP line) to 20 HP (highest-most BHP line).

Gad Zooks! There sure is a lot of information on any combined chart of Performance Curves!

And now PTOA Readers and Students have a fairly good idea of how to interpret the real world Centrifugal Pump Performance Chart of a constant speed Centrifugal Pump!

TAKE HOME MESSAGES: Once a Centrifugal Pump is purchased and installed, it may not perform optimally in the real world until it is modified and may have to be "stepped up" or "stepped down."

One way to change the performance of a Centrifugal Pump is to change the size of the Impeller. The size of the Impeller is "the diameter of the Impeller."

Once a set of TDH, Efficiency, and BHP Performance Curves for a pump have been established, correlating Performance Curves that correspond to changing the Impeller Diameter can be calculated via the Affinity Laws.

Affinity Law #1: The Capacity varies directly with the diameter of the Impeller.

Affinity Law #2: The TDH varies directly with THE SQUARE of the diameter of the Impeller.

Affinity Law #3: The Brake Horsepower of the Pump will vary directly as THE CUBE of the Impeller diameter.

There are limitations on the maximum and minimum length of an Impeller. For example, an Impeller that is too long will rub on the Cutwater of the Volute. 

The Cutwater of the Volute is the point where the spinning water  either enters the Pump Discharge or spins around the pump again.

Real world Centrifugal Pump Performance charts combine information for several sizes of Impellers and show their impact on the TDH-Capacity relationship.

For constant speed Centrifugal Pumps:

• Efficiency lines are often represented as "U" shaped lines.
• BHP lines are often represented as lines that slant downward and to the right.

 

Physical changes to the Impeller and Volute can be made by professionals to significantly change the performance of a pump. Physical changes to the Impeller and Volute are not part of the Affinity Laws and are performed by pump specialists only.

Many thanks to EngineeringToolbox.com for the use of their nifty Affinity Law Calculator for Centrifugal Pumps.

©2017 PTOA Segment 0169
PTOA Process Variable Pressure Focus Study Area
PTOA PV Pressure Rotating Equipment Focus Study

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