My head is spinning
My head is spinning
My head is spinning

("My Head is Spinning," by the Pet Shop Boys, 1993)

CHANGING PUMP PERFORMANCE WITH IMPELLER RPMs

PTOA Readers and Students just learned how Affinity Laws #1, #2, and #3 can be used to predict the change in Capacity, Total Dynamic Head (TDH), and Brake Horsepower when a Centrifugal Pump's Impeller is replaced by an Impeller with a shorter or longer diameter.

Yep!

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order already know that a longer diameter Impeller will generate a greater TDH Curve (aka Characteristic Curve) compared to a shorter diameter Impeller that is being spun around at the same speed.

And vice versa, PTOA Readers and Students likewise learned in PTOA Segment #169 that a shorter Impeller will decrease the TDH generated whilst spinning at the same speed.

An alternate method for "stepping up" or "stepping down" the performance of a Centrifugal Pump is to vary the speed of the Impeller by rotating it faster or slower.

An Impeller that is spinning faster will complete a greater amount of revolutions ... or complete circles ... over the time interval of one minute.

So an Impeller that is now completing more revolutions per minute .... rpms ... is spinning faster than it was ...

and vice versa ...

An Impeller that is completing less rpms than it was previously is spinning more slowly.

To repeat loud and clear:

• The speed of anything that is spinning around is circles is measured by how many revolutions the thing completes in a minute ... and ...
• The more rpms, the faster the speed of rotation!

RPMs are a totally different way of measuring speed when compared to driving a car really fast down a highway!

 

 

AFFINITY LAWS FOR VARYING IMPELLER SPEEDS

The nearby graphic shows the predicted performance of a Scot 57 pump with Impeller sizes that range from 5.50 to 6.88 inch.

The top most Characteristic Curve shown in the diagram is the TDH generated with a 6.88 inch Impeller over a Capacity range of 0 to 1100 gpm.

PTOA Readers and Students should notice the box of data on the middle-right side of the graphic:

The boxed data shows the (maximum) Horsepower that is required to spin the 6.88 inch Impeller at speeds which vary in increments of 500 rpm from a  low range of 1500 rpm to a high range of  3500 rpm.

The data table shows that a maximum of 2.4 Hp is needed to spin the Impeller at 1500 rpm and a maximum of 30.0 Hp is needed to spin the Impeller at 30 rpm.

Doesn't it just make sense in your gut that spinning an Impeller faster would require more Hp?

 

AFFINITY LAW #4: THE IMPACT OF RPMs ON PUMP CAPACITY

Affinity Law #4 is:

The pump Capacity varies directly with the RPM speed of the spinning Impeller.

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order will notice the similarity between Affinity Law #4 and Affinity Law #1 which was featured in PTOA Segment #169:

Affinity Law #1 stated that the pump Capacity varied directly as the diameter of the Impeller.

So PTOA Readers and Students will not be surprised to learn that the Capacity of a pump can be "stepped up" or "stepped down" by multiplying a "known" Capacity by the ratio of the "new"/"known" Impeller speed ... for example:

As stated previously above, the top TDH Curve results with a 6.88 inch diameter Impeller.

Check it out and verify that at a Capacity of 800 gpm, the TDH generated by the 6.88 inch Impeller is just real close to 150 feet.

Assume the Impeller is spinning at a known speed of 3500 rpm and then use Affinity Law #4 to predict the Capacity when the rotation speed is decreased to a new speed of 3000 rpm:

Capacity at 3000 rpm = 800 gpm *(3000 rpm/3500 rpm)

    = 800 gpm * (3000/3500) = 686 gpm

Voila!

"Stepping down" the performance of the Scot 57 Centrifugal Pump by decreasing the Impeller speed from 3500 rpm to 3000 rpm will decrease the pump Capacity from 800 gpm to 686 gpm.

Remember!

The Capacity of Centrifugal pumps can be "stepped up" using the same relationship between a "known" Capacity and rpm and a "new and faster" rotation speed.

 

AFFINITY LAW #5: THE IMPACT OF RPMs ON TDH

Affinity Law #5 can be used to determine the TDH that will be generated when the pump is "stepped up" or "stepped down" by increasing or decreasing the speed of the Impeller.

Affinity Law #5:

The TDH varies directly with THE SQUARE of the RPM speed that spins the Impeller.

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order cannot help but notice how similar Affinity Law #5 is to Affinity Law #2.

Affinity Law #2 stated that the TDH varies directly with the square of the diameter of the Impeller!

Brilliant PTOA Readers and Students can easily extrapolate and modify what they learned about Affinity Law #2 to "step down" the TDH of the Scot Pump by applying Affinity Law #5 and decreasing the Impeller speed from 3500 rpms to 3000 rpms.

First thing is to remember that ... with the 6.88 inch Impeller ... the Scot 57 pump has a Capacity of 800 gpm and a TDH of 150 feet.

Next ...

"Stepping down" the pump TDH via decreasing Impeller speed can be calculated as follows:

TDH at 3000 rpm  = 150 feet (3000 rpm)² / (3500 rpm)²

    = 150 * 0.7347 = 110 Feet

Aha!

"Stepping down" the Scot 57 pump by reducing the speed of the rotating Impeller from 3500 rpms to 3000 rpms reduces the TDH of 150 feet to 110 feet.

By selecting a few more known points on the TDH-Capacity Curve (aka Characteristic Curve) shown for the 6.88 inch Impeller, Affinity Laws #5 and #6 can be used to predict the entire 3000 rpm Characteristic Curve for the Scot 57 pump.

And don't forget!

The TDH of Centrifugal pumps can likewise be "stepped up" using the same relationship between a "known" TDH and rpm and a "new and faster" rotation speed.

 

AFFINITY LAW #6:
THE IMPACT OF RPMS ON BRAKE HORSEPOWER

Affinity Law #6 states how the Brake Horsepower will change as the speed of the Impeller is increased or decreased:

The Brake Horsepower of the Pump will vary directly with THE CUBE of the RPM speed of the spinning Impeller.

PTOA Readers and Students already know that "cubing a number" means to raise it to the power of 3 ... one more power than squaring!

And by now who is surprised to notice the similarity between Affinity Law #6 and Affinity Law #3 which states that the Brake Horsepower of the Pump will vary directly as THE CUBE of the Impeller diameter?

Ergo ...

Affinity Law #6 can be used to predict how the performance of the Scot 57 pump can be "stepped down" from 3500 rpms to 3000 rpms after first grabbing some data from the data box that is shown in the middle-right of the Scot Pump Performance Curve chart.

When the 6.88 inch Impeller is installed in the Scot 57 Pump ...

The data in the box states that a maximum BHP of 30 is required when the Impeller speed is 3500 RPMs.

So ...the

BHP required with 3000 rpm speed = 30 hp (3000 rpm)³ / (3500 rpm)³

      = 30 * (0.6297) = 18.89 = 19 hp

Hey!

Check it Out!

The calculated maximum 19 Hp predicted after "stepping down" the Scot 57 pump from 3500 to 3000 rpm matches the 19 Hp listed in the data box! That's because Affinity Law #6 was used to generate the data listed in the table!

And, of course it goes without saying...

The BHP of a Centrifugal pump can be "stepped up" using the same relationship between a "known" BHP and rpm and a "new and faster" rpm.

 

HOW DOES THE SPEED OF THE IMPELLER RPMs IMPACT THE PUMP'S EFFICIENCY?

In a future PTOA Segment, PTOA Readers and Students will learn how the design of the Impeller can also change the Characteristic Curve  of a Centrifugal pump (aka, the TDH-Capacity relationship).

Spoiler alert!

PTOA Readers and Students will learn that the Impeller is designed with vane angles which accommodate a restricted range of speed variance.

Therefore, there are Real World limits with respect to how much the Impeller's speed can be increased or decreased.

For this reason, PTOA Readers and Students can assume that the Efficiency of a Centrifugal Pump remains constant over the small step changes made to Impeller speed rotation.

 

THE REAL WORLD COMBINATION PERFORMANCE CHART
FOR THE VARIABLE SPEED PUMP

A real-world "Combination" Performance Curve Chart for a Scot 57 variable speed pump is shown nearby.

Guess what?

The Combination Performance Curve Chart for the Scot pump has the same type of information that PTOA Readers and Students observed on the Combined Performance Curve Chart for the constant speed 4BC Pump which was featured in PTOA Segment #169 and is shown below.

Both the nearby Constant Speed Performance Curve Chart for the 4BC pump and the Variable Speed Performance Curve Chart for the Scot 57 Pumps  include TDH-Capacity "Characteristic Curves" with different sizes of Impellers.

The Efficiency of both the Constant Speed 4BC Pump and the Variable Speed Scot 57 Pump are expressed as "U" shaped lines.

Both the Constant Speed 4BC Pump and the Variable Speed Scot 57 Pump represent BHP as downward-right slanting straight lines.

So...

The clues that the Scot 57 Pump Chart is for a Variable Speed pump are simply:

• The legend of the Pump states that it is Variable Speed ... which implies that it can be operated with a Variable Speed Driver/Variable Frequency Driver of some type.
• The data table in the middle right of the Scot 57 Performance Curve Chart correlates the maximum BHP that would be required as the speed of a specified Impeller is varied from 1500 to 3500 rpms whereas the 4BC Pump Chart clearly states that only one Impeller speed of 1750 rpms applies.

Yeah!

PTOA Readers and Students can now claim a familiarity with respect to being able to interpret the  Performance Curves for Variable Speed and Constant Speed Pumps!

By the way, the Affinity Laws also apply to fans!

Hang in there!

The next PTOA Segment features the last and final remaining important line on the chart of Performance Curves ... Net Positive Suction Head Required!

 

TAKE HOME MESSAGES: Once a Centrifugal Pump is purchased and installed, it may not perform optimally in the real world until it is modified by "stepping up" or "stepping down" its performance.

Affinity Laws are used to estimate the pump performance that will result after the pump is "stepped up" or "stepped down."

The previous PTOA Segment #169 featured Affinity Laws #1,#2, and #3 which are used to "step up" or "step down" pump performance by substituting longer or shorter diameter Impellers.

This PTOA Segment #170 featured Affinity Laws #4, #5, and #6 which are used to estimate pump performance after "stepping up" or "stepping down" the pump by varying the speed of the pump.

The speed of a pump is measured by how many revolutions per minute (rpms) are completed by the spinning Impeller; the greater the number of rpms, the greater the speed of the Impeller ... and vice versa.

Once a set of TDH, Efficiency, and BHP Performance Curves for a pump have been established for a pump with a specified Impeller, correlating Performance Curves can be generated by using the Affinity Laws which will predict the impact of changing the speed of Impeller rotation. These Affinity Laws are: 

• Affinity Law #4: The pump Capacity varies directly with the RPM speed of the spinning Impeller.
• Affinity Law #5: The TDH varies directly with THE SQUARE of the RPM speed of the spinning Impeller. 
• Affinity Law #6: The Brake Horsepower of the Pump varies directly with THE CUBE of the RPM speed of the spinning Impeller.

The Efficiency of a Variable Speed Pump does not change much and can be assumed to be constant no matter what the speed of Impeller rotation is. 

The above assumption can be made because ... in the Real World ... the vane angles of Impellers are designed to accommodate a small range of rotational speed. 

The Combined Performance Curve Charts for both the Constant and Variable Speed pumps are extremely similar and contain a wide range of information that characterizes pump performance.  

©2017 PTOA Segment 0170
PTOA Process Variable Pressure Focus Study Area
PTOA PV Pressure Rotating Equipment Focus Study

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