I said I just dropped in to see what condition my condition was in
Yeah
Yeah
Oh yeah

["I Just Dropped In (To See What Condition My Condition Was In)," made famous by The First Edition, but written by Mickey Newberry, 1967]

PTOA Readers and Students just learned that the Capacity of a Centrifugal Pump can exceed what is optimal and move into a Capacity range  that will cause a harmful pump problem called Cavitation.

Wouldn't the safer, more simple option be to design the pump to operate in the smack middle of the Capacity range?

The answer to the above question would be Yes Indeedo were it not for the fact that the Dynamic Head (TDH) versus Capacity relationship is not the only important relationship displayed by a Performance Curve.

Two other curves help define the optimal Capacity where the Centrifugal Pump should be operated:

• The Efficiency Curve (red curve in the nearby chart)
• The Brake Horsepower Curve (BHP Curve ... the green curve in the nearby chart).

All PTOA Readers and Students should be able to look at the nearby chart of Performance Curves and understand that every Capacity point on the chart's X-Axis has a corresponding and unique TDH, Efficiency, and BHP point.

In other words ...

For every Capacity of throughput for the pump in gpm ... there is a definite Pump Efficiency that corresponds to a specific, required TDH which is only achievable with a pump that is selected to provide the designated Brake Horsepower (BHP).

These three points define the "Condition of the Pump" at every value of the Centrifugal Pump's Capacity.

By the time PTOA Readers and Students complete this PTOA Segment #168 they will be able to determine the optimal Condition of the Pump from assessing the changes observed between Pump Efficiency, TDH, and Brake Horsepower (BHP) as the pump Capacity changes.

This PTOA Segment also features background information regarding the meaning and definition of:

• Power
• Hydraulic horsepower, and
• Efficiency

There's one other noteworthy curve that will be discussed in a future PTOA Segment yet shows up on most Performance charts:

• Net Positive Suction Head Required (NPSHr)

NPSHr will be featured soon in the PTOA Segment that focusses on Cavitation.

 

ISOLATING THE CAPACITY-TDH RELATIONSHIP

The nearby graphic isolates the TDH-Capacity relationship.

The TDH-Capacity curve is sometimes called The Pump Characteristic Curve.

Who amongst the brilliant PTOA Readers and Students remembers that the change in Capacity ...

from 0 gpm on the left hand side of the X axis to the maximum amount on the right hand side  ...

is what happens in the real world when the Outside Process Operator opens the Discharge Valve from 'totally blocked in' position to 100% open?

So guess what?

Friction Losses explain why the head that the pump can discharge (aka TDH) decreases as the Capacity increases!

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order are not surprised to connect these dots because they recently learned the following fun facts about PV Pressure Losses in PTOA Segment #165:

• PV Pressure Losses caused by friction happen any time fluids are flowing through pipes, fittings, and all types of hardware.
• PV Pressure Losses are proportional to the square of the flowrate (aka the Pump Capacity).

Therefore ...

The greater the Capacity on the X-axis ...

The greater the PV Pressure losses due to Friction ... and thus the arcing downward shape of the TDH curve!

 

HORSEPOWER DEFINED  

The Brake Horsepower Curve (BHP Curve) is another unique point that helps define the  Pump's Condition.

There are two prerequisites that lead up to understanding BHP:

• Understanding the concept of hydraulic horsepower.
• Understanding the concept of machine Efficiency.

And prior to learning the above concepts ...

Everyone must understand what is meant by the phrase "horsepower."

What is "Horsepower?"

The Industrial Revolution (roughly 1760-1840) is described as a time wherein the handiwork of Humankind was replaced by machines ...

which is still a timely subject considering Artificial Intelligence is predicted to replace large segments of manual labor during the 21st century!

In the 1780s, Scottish inventor James Watt promoted the use of his steam engine by proving how much more work the steam engine could perform compared to the work that horses performed while hauling water out of coal mines.

Before Watt could prove how much more powerful his steam engine was he needed to develop the basis for measuring "power" ... which is the amount of work performed over a unit of time.

Watt determined that a horse can vertically lift a weight of 550 lbs a distance of one foot over a time interval of one second.

Watt's mathematical description-definition of hydraulic horsepower can be converted to the time basis of one minute via the following conversion:

1 hp = 550 ft-lbf/sec  * 60 sec/1 min =  33,000 ft-lb_f/min

1 hp = 33,000 ft-lb_f/min

Note the units that express hydraulic horsepower are:

(height-weight) / time.

Every PTOA Reader and Student who reads the PTOA Segments in the intended sequential order already knows that "weight" is simply a mass that has the force of gravity acting upon it ...

that concept was explained in PTOA Segment #143.

Ergo, "hydraulic horsepower" is a unit of power that complies to the rule that everything is derived from the three basic units of measurement ... mass, length, and time ... as was mentioned way, way back in PTOA Segment #60.

Fun fact:

A weight lifter raising a bar bell over his/her head is likewise expending horsepower by lifting the weight over a vertical distance in a short amount of time.

Yabba Dabba Do!

Time to apply all of the above to understanding:

• Hydraulic Horsepower of a Centrifugal Pump.
• Efficiency and Pump Efficiency.
• Brake Horsepower (BHP).

Wow!

There sure is a lot of background information to learn before learning how to identify the optimal Condition of the Pump from a chart of Performance Curves!

 

HYDRAULIC HORSEPOWER OF A CENTRIFUGAL PUMP

An improved yet equivalent expression for "hydraulic horsepower" that applies to pumps is:

The amount of work required to change a liquid from a beginning elevation, Pressure, and velocity to a final elevation, Pressure, and velocity over a set period of time.

It doesn't take much imagination to figure out that the power of a Centrifugal Pump moves a mass of liquid from the Suction-side Head elevation, Suction-side Pressure, and Suction-side Flowrate/Capacity to the Discharge-side Head, Discharge-side Pressure, and Discharge-side Flowrate/Capacity.

Otherwise stated ...

The hydraulic horsepower of the liquid being pumped can be thought of as the is the increased energy state of the liquid at Pump Discharge because of a change in elevation (aka TDH), change in Pressure, and change in velocity (aka Flowrate/Capacity) between the Discharge and Suction.

The generalized expression that defines Hp ...

Hp = (Weight)(Height) ÷ (Time)

Can be converted into an expression that describes the hydraulic horsepower transferred into the pumped liquid:

Hp = [(Capacity in gal/min) * (TDH in ft) * (Spec.Gravity of Liquid)]

÷ 3960

Does a Process Operator need to memorize the above defining expression for hydraulic horsepower to perform his/her job well?

Heck No!

Hydraulic horsepower doesn't even appear on the chart of Performance Curves ... it's Brake Horsepower that appears on the chart!

Just be mindful that:

• Hydraulic horsepower greatly impacts the Brake Horsepower Curve (as will be described soon in this PTOA Segment).
• The Centrifugal Pump's hydraulic horsepower (Hp) is influenced by two offsetting factors ... the Pump's  Capacity and TDH.

 

EFFICIENCY DEFINED FOR ANY MACHINE

What is meant by a Machine's "Efficiency?"

Who is John Galt?

John Galt is/was a make-believe protagonist  conjured up by author Ayn Rand for her 1957 rant entitled "Atlas Shrugged."  John Galt supposedly defied the laws of physics and invented a "frictionless motor."

Galt's invention is as much a fairy tale as Goldilocks' wrong choice of the perfect porridge featured in PTOA Segment #79 because the Universe has decreed that some power shall always be sacrificed to friction and the emission of noises. Therefore:

There is no such thing as a 100% efficient machine!

PTOA Readers and Students who can access the below link will be mesmerized by the myriad of simple mechanical machines incorporated into OK-Go's Paint Gun Machine You Tube that was created to promote their song "This Too Shall Pass."

Note that:

• From the initial push of the red toy truck and onward ... each of the simple machines had to be designed to operate with sufficient power to both overcome the friction that results between any rubbing surfaces AND transfer enough left over power to keep the machine going.
• Hydrostatic head is used as a power source within the OK Go Paint Gun Machine where the colorful liquids dribble through tubing.

ACCESS HERE FOR OK GO's "THIS TOO SHALL PASS"  PAINT BALL MACHINE

 

EFFICIENCY DEFINED FOR A CENTRIFUGAL PUMP

No Centrifugal Pump has 100% Efficiency either.

Otherwise stated ...

All of the power that the driver does to spin the shaft and impeller will not be transferred into the pumped liquid. An 80% Efficiency for an operating pump is darn good!

The Efficiency of the Centrifugal Pump will be reduced by:

• Friction Losses within the pump as the liquid flows through the pump.
• Turbulence of the liquid in the pump.
• Friction Losses in the packing and bearings.

The Efficiency of the Pump can be calculated using the below equation:

Hydraulic Hp of the pumped liquid

÷

Hp put into the machine to make it operate

Which can be rewritten as shown below by inserting the definition PTOA Readers and Students just learned for hydraulic horsepower:

Efficiency (expressed as a Decimal Fraction) =

[Hp = [(Cap in gal/min) * (TDH in ft) * (Sp.Gr of Liquid)]÷ 3960]

÷

Hp of the Driver 

Does a Process Operator need to memorize the above defining expression for pump Efficiency to perform his/her job well?

Heck No!

But a Process Operator should be vaguely aware of these Pump Efficiency phenomena:

• The Efficiency of a Centrifugal Pump is greatly impacted by hydraulic horsepower (and thus TDH and Capacity).
• The expression for pump Efficiency will ALWAYS be less than 1.0!
• However, Pump Efficiency is often multiplied by 100 to be expressed as a Percentage on the Efficiency Performance Curve.

A typical Pump Efficiency Curve in red is featured on the nearby chart of Performance Curves.

Naturally, Pump Efficiency= 0 at 0 Capacity gpm because ... with no flow through the pump ... the pump is not in the process of changing the elevation, Pressure, or velocity of the liquid.

The Pump Efficiency Curve increases with increasing pump Capacity up until the increase in Capacity creates large friction losses that make the Efficiency Curve arc downward.

Unless told otherwise, PTOA Readers and Students should assume the chart of Performance Curves is describing a Centrifugal Pump that does not have a variable speed driver.

Therefore ...

Operating the pump at any point other than the maximum Efficiency-Capacity condition would waste the utility expense that pays for rotating the shaft of the pump.

Thus:

The optimal Capacity to operate a Centrifugal Pump is at the pump Condition described by the maximum Pump Efficiency ...which is just prior to where the Efficiency begins to decrease. 

The Pump Efficiency Curve in some Performance charts appears to flatten out a bit over a Capacity range. In that case, the optimal Condition of the Pump is the Capacity with the maximum Pump Efficiency AND greatest TDH. The TDH Curve will never flatten out and will always be plunging downward with increased Capacity!

 

BRAKE HORSEPOWER (BHP)

Let's be honest.

"Brake Horsepower" is a confusing term that makes one think of stopping power or something like that. Some committee should have decreed a new name by now.

The modifier "Brake" refers to the instrument that is used to scientifically measure Brake Horsepower ... the "brake dynamometer."

Brake Horsepower (BHP) is the horsepower an engine could supply before any losses in power occur.

Why measure BHP instead of Hp?

Remember how each of the simple machines in the OK Go Paint Gun Machine had to overcome friction AND deliver enough punch to keep the machine working?

Likewise ...

The person who selects the Centrifugal Pump must size the pump to provide the amount of horsepower needed to move the required amount of liquid AND account for power losses throughout the machine.

BHP is simply calculated by dividing the Hydraulic Hp of the liquid by the pump's Efficiency (expressed as a decimal fraction):

BHP = Hp ÷ Pump Efficiency

Because Pump Efficiency is always less than one, BHP will always be GREATER THAN the Hydraulic Horsepower.

PTOA Readers and Students who desire to understand how BHP is calculated from Pump Efficiency and hydraulic horsepower can access the below link:

Example BHP Calculation

Does the Process Operator need to memorize the above definition/expression for BHP to perform his/her job well?

Heck No!

However, the Process Operator should be familiar with the meaning of Pump Efficiency and BHP and understand that the two are intimately related ...  BHP is determined by dividing Hp by Pump Efficiency.

 

IDENTIFYING THE OPTIMAL THE CONDITION OF A PUMP

Shazam!

PTOA Readers and Students who have not dozed off by this point have now learned all the concepts that support a chart of Performance Curves which will be supplied by the pump's manufacturer.

The optimal Condition of the Pump can be determine from interpreting the chart of Performance Curves.

The below chart of Performance Curves is for a Centrifugal Pump that has an Impeller spinning at 1750 revolutions per minute (rpm).

The diameter size of the Impeller has a major impact on the Performance Curves; the magnitude of the impact will be featured in an upcoming PTOA Segment.

All PTOA Readers and Students should confirm that the optimal operating condition for this Centrifugal Pump is revealed to be where the:

• Capacity of 1100 gpm and corresponding TDH of 94 feet because that's where ...
• Efficiency is at the maximum 84% ... which will require a
• BHP of 34 when selecting this style of pump for a pumping service.

 

TAKE HOME MESSAGES: Every chart of Performance Curves shows the unique values of TDH, Pump Efficiency, and BHP that extend across the range of Pump Capacity.

Each  TDH-Pump Efficiency-BHP-Capacity family describes a  Condition of the Pump.

Because of the assumption that the driver is not a variable speed driver ...

The optimal Condition of a Pump is where the Capacity is at maximum Efficiency which identifies the TDH requirement. To achieve the specified TDH the pump must be sized for the Brake Horsepower (BHP) that works at the Maximum Efficiency-TDH condition.

The Efficiency of a Pump is the hydraulic horsepower of the pumped liquid divided by the energy used to make the pump work.

No machine is 100% Efficient. No machine can transfer or perform all of the work it is built to do because of power losses.

The Efficiency of a Pump will be a decimal fraction that is less than 1.0; Note the Efficiency Curve on a Performance chart is typically expressed as a percentage.

Brake Horsepower is the power an engine has before power losses occur in the operation of the machine.

In a pump, the Brake Horsepower will always be greater than the hydraulic horsepower transferred into the pumped liquid.

Understanding the terms "Efficiency" and "Brake Horsepower" required understanding these terms:

• "Power" is the rate of doing work.
• The units of hydraulic horsepower are Hp.
• Hp has been derived and defined from calculating how much work was done by moving a mass over a vertical distance in a specified amount of time.
• Hydraulic horsepower for a pump refers to the work performed when a liquid is moved from a beginning elevation, Pressure, and Velocity to an ending elevation, Pressure and velocity.

The TDH Curve is sometimes called the pump's "Characteristic Curve."

©2017 PTOA Segment 0168
PTOA Process Variable Pressure Focus Study Area
PTOA PV Pressure Rotating Equipment Focus Study

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