Scary monsters, super creeps
Keep me running, running scared
Scary monsters, super creeps
Keep me running, running scared

("Scary Monsters," by David Bowie, 1980)

 

INTRODUCTION TO CENTRIFUGAL PUMP PERFORMANCE CURVES

Modern Plant Managers want modern Process Operators to understand why it is important to operate Centrifugal Pumps at their optimal flow through rate.

Process Operators who do not  understand the basics of Centrifugal Pump operation may inadvertently cause the pump to cavitate.

The best way to illustrate the optimal pump operating range is to learn how to interpret the myriad of lines that appear on a Centrifugal Pump Performance Curve.

The X-axis on every Performance Curve is the Capacity of the pump, aka the flow of liquid that the pump can handle in gallons per minute (gpm).

For example, the Capacity scale of the nearby Performance Curve could be 0 gpm on the far left side of the X-axis to 1400 gpm on the far right side.

The Total Head is shown plotted on the nearest Y-axis of the nearby Centrifugal Pump Performance Curve.

The Total Head curve is the blue curve that decreases in an arc as the Capacity of the pump increases.

Unlike the pump's Capacity, Total Head takes a bit more brainwork to understand.

The goal of this PTOA Segment #166 is to define the Total  Head that a pump must achieve to successfully add sufficient PV Pressure energy into the liquid so that it can get to where it is going and do what it is supposed to do.   

Otherwise stated:

The Total Head is the difference in PV Pressure measured between the Pump Discharge and Pump Suction.

The word "Total" in "Total Head" is a big hint that "Total Head" is derived from several contributing sources.

Righteoo!

Albeit invisible, there is a Three-Headed Centrifugal Pump Monster on both the Suction and Discharge sides of any Centrifugal Pump.

The Total Head of a Centrifugal Pump is determined after quantifying these three sources that contribute to the Total Suction-side Head and the Total Discharge-side Head of any Centrifugal Pump:

• The Static Head
• The Pressure Head
• The Friction Loss Head

 

QUICKIE REVIEW OF HYDROSTATIC HEAD

In PTOA Segments #146 and #147, PTOA Readers and Students learned all about hydrostatic head.

In fact, PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order used the hydrostatic head of sea water at the Strait of Gibraltar to determine how much pressure was bearing down upon the hull of U Boat 96 via this expression for hydrostatic Pressure:

Pressure (psi) =  SG *  0.433 psi/1 foot   *  h (feet)

where:

• SG means Specific Gravity of the liquid, a dimensionless number.
• h is the hydrostatic head in feet of the liquid that is exerting Pressure.

The above expression can be easily rearranged to find the hydrostatic head when the Pressure in psi is known:

h (in feet) = Pressure (psi) / (SG * 0. 433  psi/foot)

For example:

1 psi of water is created by a hydrostatic head of 2.31 feet

because:

h (in feet) = 1 psi / (1.0 * 0.433 psi/foot)

           = (1) / (1.0 * 0.433) = 2.31

Hey! That's a handy conversion factor to know:

2.31 Static Head Water in Feet  / 1 psi  Water Pressure 

Because if 1 psi of water is created by a hydrostatic head of 2.31 feet, that means any multiple of Pressure in psi can be created by an equal multiple of head in feet!

For example:

10 psi water = 23.1 Static Head in Feet

because:

h (in feet) = 10 psi / (1.0 * 0.433 psi/foot)

                                        = (10) / (1.0 * 0.433) = 23.1

and

100 psi water = 231 Static Head in Feet

because:

h (in feet) = 100 psi / (1.0 * 0.433 psi/foot)

                                        = (100) / (1.0 * 0.433) = 231

HEAD #1:  THE STATIC HEAD

The first head of the Three Headed Centrifugal Pump Monster is the Static Head which is created by any standing vertical distance of liquid.

Static Suction Head of a Centrifugal Pump

In PTOA Segment #164, PTOA Readers and Students learned that the Typical Pump Installation Set Up includes a tank which stores the inventory of liquid that will soon be fed into the Pump Suction Line and thence to the Pump Suction.

The nearby graphic illustrates that the Static Suction Head is the vertical distance from the Centerline of the pump's Suction Line to the liquid level in the Suction-side tank.

In other words, the Static Suction Head includes the hydrostatic head of the liquid contained in the Suction-side tank plus the hydrostatic head of the liquid that is contained in the liquid-filled vertical piping.

The definition of Static Suction Head makes perfect sense because ....

as any brilliant PTOA Reader and Student can recite by heart ...

"the Pressure exerted by a liquid only depends upon the height and the density of the liquid ... not the volume or shape of the container holding the liquid."

Quantifying Static Suction Head is easy because it is just the depth of the contained liquid added to the length of vertical pipe that extends from the bottom of the tank.

For example ... assume:

• There is 3 feet of liquid contained in the Suction-side Tank.
• The vertical distance from the bottom of the Suction-side Tank to the elbow in the Suction Pipe Line is 5 feet.

Then ... voila!

Static Suction Head = 3 + 5 Feet!

 

Static Discharge Head

Extending what was just learned about Static Suction Head to the other side of the pump ...

PTOA Readers and Students are probably not surprised to learn that  the Static Discharge Head is the vertical distance between Centerline of the Pump Suction Pipe and the top of the liquid level contained in the Discharge-side Tank.

Static Discharge Head is also easy to determine!

If the vertical distance between the Centerline of the Suction Pipe and the top of the Discharge-side Tank is 25 feet, then:

The Static Discharge Head is 25 feet!

Now that PTOA Readers and Students have been made aware of the Static Head Monster that lives in the Suction-side and Discharge-side of a Centrifugal Pump ... it's time to learn about Pressure Head.

 

HEAD #2:  PRESSURE HEAD

The Suction-side and Discharge-side tanks in the above drawings indicate that the tanks are open to atmospheric pressure because they are not enclosed.

When the Suction-side and Discharge-side Tanks/Vessels/Receivers are enclosed, the Pressure Head must be determined.

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order already learned in PTOA Segments #147 and #162 that the vapor space above any enclosed tank is occupied by either the vapor of the contained liquid or a gas blanket (like nitrogen or natural gas).

Either way, the vapors or gas blanket generate a pressure above the  liquid level.

In pump lingo,  when the vapor or blanket gas pressure is converted into equivalent feet, the outcome is called a  "Pressure Head."

 

Assume the Suction-side tank in the graphic above has a 25 psig gas blanket.

Since 1 psi is equal to 2.31 feet of water ...

the Pressure Head of the Suction-side tank is:

h (in feet) = 25 psig * (2.31 feet H2O)/1 psig

                                      = 57.8 feet

The Discharge-side Tank/Vessel/Receptacle will most likely also have a vapor space occupied by vapor or a gas blanket.

The Discharge-side Tank/Vessel/Receptacle Pressure Head is calculated exactly as shown above for the Suction-side Tank.

What If the Vapor Space Is Measured in PSIA?

What happens if the vapor space pressure is measured in units of Absolute Pressure ... psia?

In that case the first step is to convert the vapor space pressure measurement into the same basis that will be used to eventually determine the Total Head.

In the vast majority of cases on Earth, gauge pressure is the basis of measurement.

Ergo, the Absolute Pressure measurement in psia must first be converted into a gauge pressure, psig.

PTOA Readers and Students learned in PTOA Segment #150 that:

P_abs = P_gauge + P_atm

and that P_atm    is equal to 14.7 psi and 101.3 kPa at sea level.

To determine P_gauge the above expression can be rearranged:

P_gauge = P_abs - P_atm

Ergo ... if the Suction-side vapor space pressure was measured as 25 psia, the gauge pressure equivalent is:

P_gauge = 25 - 14.7 = 10.3 psig

So now the conversion to Pressure Head can occur:

h = (2.31 feet / psig) * 10.3 psig = 23.8 feet

Aha! It is time to learn about the third and last head of the Three Headed Centrifugal Pump Monster ... Friction Head!

 

HEAD #3: FRICTION HEAD

PTOA Readers and Students very recently learned in PTOA Segment #165 that just the action of flowing through a pipe causes a liquid to lose some of the PV Pressure to friction losses.

For example ... in the below Typical Pump Installation Set Up ...

Friction losses will occur:

• In the pipe that extends from the Tank Bottom to the Pump Suction.
• In the elbow of pipe that directs the flow from the vertical to the horizontal plane.
• In the Suction Gate Valve.
• At the Reducer prior to Pump Suction.

The "friction factors" that are assigned to  pipes, pipe fittings, valves, etc have been quantified by nerdy engineer-scientists and can be found in resources such as Crane's Technical Paper #410.

However, no PTOA Reader or Student needs to invest in such resources because they are used in the design phase of the Processing Facility, not operating phase.

Generally speaking, the factors that determine the magnitude of the "friction factor" assigned to hardware are:

• The pipe diameter.
• The roughness of the pipe's interior wall.
• The age condition of the pipe material.
• The total length that the liquid travels through the pipe.

Naturally ... the viscosity of the liquid impacts the magnitude of the Friction Loss, but this factor is a characteristic of the liquid ... not the pipe that the liquid is flowing through.

Your Mentor just wants PTOA Readers and Students to be aware of where the statements related to quantified friction losses come from.

For now friction losses will simply be stated as a specific amount of Friction Head expressed in feet.

 

TOTAL HEAD =
(TOTAL DISCHARGE HEAD)  - (TOTAL SUCTION HEAD)

Okay! PTOA Readers and Students now have sufficient knowledge to calculate the Total Head of a Centrifugal Pump!

Total Head = (Total Discharge Head) - (Total Suction Head)

First Step: Determine Total Suction Head

Total Suction Head is determined stepwise by:

• Adding Static Head to Pressure Head ... then
• Subtracting Friction Head from the above total.

Who amongst the brilliant PTOA Readers and Students can visualize that the Suction-side Static Head and Pressure Head in the nearby Typical Pump Installation Set Up are beneficial to the Centrifugal Pump because they help add PV Pressure to the liquid by just gravity and not any applied power?

However, the Suction-side Friction Head decreases the amount of PV Pressure on the Suction Side of the Centrifugal Pump.

So here's an example of ...

How to Calculate Total Suction Head for the Centrifugal Pump shown installed below:

Given:

• There is 7 feet of water in the Suction-side Tank.
• The vertical piping from the bottom of the Suction-side Tank and the elbow in the piping is 3 feet.
• The vapor space pressure in the Suction-side Tank is 64.7 psia.
• The friction losses in the Suction-side piping equal 1.3 feet Friction Head Loss.

Then:

1. Suction Static Head = 7 + 3 = 10 feet.
2. Suction Pressure Head = (34.7 psia  -14.7 psi ) = 20 psig * 2.31 feet/psi = 46.2 feet.
3. Friction Head = 1.3 feet

Thus:

Total Suction Head = (10 + 46.2)  - 1.3  = 54.9 ft

 

Second Step: Determine Total Discharge Head

Total Discharge Head is determined by adding:

• Discharge Static Head.
• Discharge Pressure Head.
• Discharge Friction Head.

Here's an example of ...

How to Calculate Total Discharge Head for the Centrifugal Pump shown installed below:

Given:

• The water level in the Discharge-side Tank is 20 feet.
• The vertical distance from the Centerline of the Suction Line and the bottom of the tank is 40 feet.
• The vapor space pressure in the Discharge-side Tank is 100 psig.
• The friction losses caused by the fluid flowing through the piping and check valve and gate valve equals 17.6 feet Friction Head.

Then:

1. Discharge Static Head = 20 feet + 40 feet = 60 feet.
2. Pressure Head = 100 psig * 2.31 feet /psi = 231 feet
3. Friction Head = 17.6 feet

Thus:

Total Discharge Head = (60 + 231 + 17.6)  = 308.6 feet

 

Ta-Dah! Finally Ready to Calculate Total Head!

Total Head = (Total Discharge Head) - (Total Suction Head)

For example ... given:

Total Discharge Head = 308.6 feet

Total Suction Head = 54.9 feet

Then:

Total Head = 308.6 - 54.9 = 253.7 feet

Gosh, it has taken so long to get to this point who remembers what Total Head means?

A Total Head of 253.7 feet means that an equivalent amount of PV Pressure energy must be added into the pumped liquid so that it can be distributed where it needs to go to do what it needs to do!

Hey! A Total Head of 253.7 feet means (253.7 * 2.31) = 586 psi must be added to the liquid flowing through the pump!

Note that the Total Head decreases in an arc as the Capacity of the pump increases.

The pump described by the nearby Performance Curve was designed for the horizontal Total Head and vertical Capacity combination indicated by the black triangle.

The optimal Total Head and Capacity is always closely associated with the optimal Pump Efficiency. Pump Efficiency is shown as a red line in the nearby Performance Curve.

Mission Accomplished!

All PTOA Readers and Students now understand what goes into the determination of Total Head for a Centrifugal Pump!

Now there's just one more thing to cover for the Not So Typical Pump Installation Set Up!

 

HOW TO DETERMINE TOTAL HEAD FOR LIFTING PUMPS

"Static Suction Head" changes into "Static Suction Lift" when the liquid in the Suction-side Tank/Reservoir is situated vertically below the Centrifugal Pump.

The nearby drawing shows a "Static Suction Head" pump installation on the left side and a "Static Suction Lift" pump installation on the right side.

Both Static Suction Head and Static Suction Lift are the vertical distance between the liquid surface and the Centerline of the pump's Suction Line.

However ...

Note that the Centrifugal Pump on the right must perform more work on the pumped liquid because it doesn't have the benefit of gravity contributing to the Static Suction Head or Pressure Head.

Ergo ...

The Static Suction Lift, Suction-side Pressure Head, and Suction-side Friction Head of a lifting pump are all negative ... and thus end up being added to the Total Discharge Head to determine Total Head!

Uh-oh Fred's sweating.

Here's an example for you, Fred:

Assume the following bullet items apply to the lifting pump installation shown on the right side of the nearby diagram:

• Suction Static Head = -10 feet
• Suction Pressure Head = 0 psig because the Suction Tank is at Atmospheric Pressure.
• Suction Friction Head = -1.3 feet.

Therefore Total Suction Head = -11.3 feet

• Discharge Static Head = 60 feet
• Discharge Pressure Head = 26 psig * 2.31 = 60 feet
• Discharge Friction Head = 17.6 feet

Therefore Total Discharge Head = 60 + 60 + 17.6  = 137.6 feet

Next ...

Total Head is calculated exactly as before ... yet beware that a subtracting a negative is the same as adding!

Total Head = (Total Discharge Head)  -  (Total Suction Head)

= 137.6 - (-11.3)

=  137.6 + 11.3 = 148.9 feet

The lift pump must add the equivalent of 149 feet of PV Pressure energy to the liquid to get it where it needs to go!

Hey! That's 148.9 * 2.31 = 344 psi!

 

TAKE HOME MESSAGES: PTOA Readers and Students were introduced to Centrifugal Pump Performance Curves as a first step to learning how to operate a Centrifugal Pump in the optimal range. 

Every Centrifugal Pump is supplied to the Processing Facility with its own Performance Curve.

A Centrifugal Pump Performance Curve includes the relationship between the pump's Capacity and Total Head.

In the USA, the Capacity of a pump is expressed in units of gallons per minute, gpm. 

The Total Head of a Centrifugal Pump is defined:

Total Discharge Head - Total Suction Head

The Total Head of a Centrifugal Pump is the PV Pressure that must be added to the liquid by the pump ... expressed in units of feet.

The three components that go into the determination of both Total Suction Head and Total Discharge Head were featured:

• Static Head,
• Pressure Head.
• Friction Heat.

Both the Static Suction Head and Static Discharge Head are determined from the Centerline of the Pump Suction Line.

Before converting into the head equivalent of pressure, all the components of Static, Pressure, and Friction Head must be on the same basis ... which is typically gauge pressure. 

The conversion factor 2.31 feet / 1 psi water is used to convert Pressure Head from the pressure measured in the vapor space of a contained liquid.

When determining Total Head for a lifting pump it is important to remember that subtracting a negative means adding!

©2017 PTOA Segment 0166
PTOA Process Variable Pressure Focus Study Area
PTOA PV Pressure Rotating Equipment Focus Study

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