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# Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

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## Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Hi All,

I want to tabulate the pump efficiency vs. flow rate for a pump that I am doing power requirement calculation. As you can see in the attached pump curve, the efficiency curves are the looping curve extending over a range of flow rates. I want to tabulate the pump efficiency vs. flow rate and use this table to accurately calculate the pump shaft power and the full load amps for the motor. I looking to get a parabolic curve with the maximum pump efficiency at a certain flow rate. How do I do that?. Can I ask the pump manufacturer?. Does the pump efficiency vary with impeller size and RPM?.

Also does the pump efficiency change with the system resistance. in my case the duty point is at 3046 gpm at 75 ft head. From the pump curve the pump efficiency is 83%. Now if I lower the system resistance by increasing the discharge line size from 10" to 12" the head developed reduces the duty point moves to the right. Depending on where the duty point the pump efficiency could either increase or decrease. I will calculate the duty point for this scenario shortly.

Thanks and Regards,
Pavan Kumar

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

How to do it?

Read it off the curve then tabulate it and create a graph.

Yes the efficiency changes with impellor diameter - look at the pump curve.

Yes the efficiency will change if you change the flow and head. Look at the curve.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

Hi,
An equation developed by C.R Branan in Rules of thumb for chemical engineer's 4th edition
Eff= 80 -0.2855*F +3.78E-04*F*G -2.38e-07*F*G^2 +5.39E-04*F^2 -6.39e-07*F^2*G +4E-10*F^2G^2
Eff: pump percentage efficiency
F: Developed HEAD (TDH), ft
G: flow, GPM
range
F=50-300 ft
G=100-1000 GPM

Hope this helps
Pierre

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Hi pierreick,

Thank you as always for providing me good reference. However my flow range is 2000-3000 US gpm and this equation will not be accurate. I can use this equation for cases where it will apply. Can you provide more references to understand about how pump efficiency varies with impeller diameter, speed and head.

Thanks and Regards,
Pavan Kumar

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

Efficiency to me has always been a measured set of values, not really a calculation. I don't doubt that the equation above can be used to get you in the right ball park, i.e. 65% not 50%, but there are far too many variables not listed there to use it for anything other than an initial estimate. different pumps at the same flow and head will have very different efficiencies. IMHO.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Hi LittleInch,

I agree with you that there are many variables that will affect the pump efficiency than just flow rate and head. I can manually read the efficiency curve and get the efficiency at the duty point. We are increasing the impeller size on the pump from the current 10.3" to 13.5" to get the required head and the flow. I have done piping friction and head loss calculations for my system and found the duty point. This duty point is at full capacity. We are also going to use a VSD to lower or increase the speed of the pump. My question is when the pump curve shifts lower or higher do I still read efficiency from the same efficiency curve for 13.5" or do I have to as vendor for different efficiency curves for different speeds. I want to get good understanding of this as this will affect my power consumption and the full load amps. Any references that you can provide will be very helpful.

Also could you tell me if I can use affinity laws for impeller diameter increase at constant speed and speed increase at constant impeller diameter get the modified pump curve and what is the limit up to which this is accurate. I heard someone say beyond 3% increase in impeller trim then the affinity won't be correct. Not sure if this applied to speed too?

Thanks and Regards,
Pavan Kumar

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

I think you need to ask the vendor for curves at different speeds.

It's better this way than using the affinity laws. Affinity laws should be good for 20-25% change I think - nothing is accurate to 3%, even the pump curve.

I think whoever said that was getting confused with what the accuracy of a pump curve has to be unless you get a specific pump curve test for your particular pump.

Also don't forget to include the 6-8% loss on a VFD drive. Quite often a simple control valve will be more efficient to control flow and pressure than a VFD. All depends on what your system curve looks like.

What is your new duty point?

If you're at the far end on the right hand side, be aware that reducing speed impacts max flow as well.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

A couple vendors have web based software that will let you generate the curves, even at different speeds. Hopefully, your pump is from one of these vendors.

Good Luck,
Latexman

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Hi Littleinch,

#### Quote (Littleinch)

I think you need to ask the vendor for curves at different speeds.

It's better this way than using the affinity laws. Affinity laws should be good for 20-25% change I think - nothing is accurate to 3%, even the pump curve. Are you saying that I can use Affinity laws when the RPM or impeller size is increased or decreased by 20-25%. For example in my case we are increasing the impeller size from 10.3" to 13.5" which is 31% increase (= 13.5-10.3)*100/10.3). So that means I cannnot use affinity laws to get the pump curve for 13.5" impeller from the pump curve at 10.3" impeller at the same RPM of 1750?.

I think whoever said that was getting confused with what the accuracy of a pump curve has to be unless you get a specific pump curve test for your particular pump. Did not understand what you tried to say here.

Also don't forget to include the 6-8% loss on a VFD drive. Quite often a simple control valve will be more efficient to control flow and pressure than a VFD. All depends on what your system curve looks like. So if the power supplied to the motor is 100 HP then 6-8% of the VFD the actual power supplied will be 92-94 HP?

What is your new duty point? My duty point with 13.5" impeller is at 3046 US gpm at 75 ft head.
The efficiency at this duty point for 13.5" impeller is 83%. The shaft power required is

P = m * DH / (eff*550)
where m is the mass flow rate

Q=3046 US gpm
Density - 61.64 lb/ft3
DH = Head - 75 ft
Pump Eff = 83%

P = (3046*0.133681/60)*61.64* 75/(0.83*550) = 68.7 HP

With 10% power loss for VFD then the total power required = 1.10*68.7 = 69.8 HP, the current draw would be 68.56 Amperes.

And if Motor EFF,nm = 93% and PF =0.82

I = Pshaft*746 / (1.73*V*nm*PF)= 68.7*746/(1.732*575*0.93*0.82) = 67 Amperes.

Full Load amps will be 67 amperes assuming the full load motor efficiency and PF I took there are correct.

the BEP is at 87% efficiency from the pump curve so I will be within 80 to 120 % of BEP, the recommended range. My question though is that we will use a VFD to lower the speed as per capacity requirement of the unit, then I want to know how the efficiency will change. Should I ask the vendor to issue me efficiency curves for a few speeds and I interpolate for the efficiency if the speed I use is between these curves?.

If you're at the far end on the right hand side, be aware that reducing speed impacts max flow as well.
I am not operating far too right. Please see the system and pump curve attached.

As TiCl4 told me in the last thread that the power varies as cube of speed with efficiency not varying much.

so if N2= 1200 RPM (say)

P2=P1*(N2/N1)^3 = 68*(1200/1750)^3= 21.92 HP

At part load

I = 21.92*746/(1.732*575*0.93*0.82) = 21.53 Amperes

https://www.eng-tips.com/viewthread.cfm?qid=493196

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### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

Just remember that the curve that you are looking at is "typical" and not for your specific pump.
I have seen +/- a few percent in very well built pumps, I hate to think of the variation is lower quality units

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

https://www.av8rdas.com/affinity-laws.html

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

I can't do much better than the explanation in the link by mr 44.

what I was saying that if you take it ( the affinity laws) too far, then other factors come into play which makes the calculation result less and less accurate. SO in your case - 31%, your accuracy is likely to be 10-15%. But you don't need it if you've got a pump curve...

So an example. on your pump curve at say 2000 gpm that's 40 ft diff head. Extrapolating up to 13.5, that's a flow of 2620 GPM and head of 68 ft. The pump curve says at 2620 at 13.5" the head is about 75ft. So a difference of ~10%. Not bad, but not super accurate either.

The pump curve that is generated by the vendor before purchase is a "generic" curve or set of data that they adjust to match your duty point. The actual pump you get has a tolerance of usually 3-5% and still be within validity.

VFDs suck about 8% of the power that goes in as heat. So if your motor needs / uses 100kW, the electrical input into the VFD will be about 108kW.

In your example calc 1.1 x 68.7 HP = 75.57. I don't know how you got the answer to be 69.8....

I think the efficiency changes a bit with speed, but better to ask the vendor of a set of curves at your min, normal and max speeds.

Don't forget the head falls as a square, so you would only have ~35ft head at 1200 rpm so you would be flowing at about 2000 gpm based on your system curve

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Hi EdStainless,

Do you mean to say that the correct curve for my pump in question is given only after testing. I don't think any vendor is doing this these days. They simple use their software to print the pump characteristic curves.

HI 1503-44,

The link you provided is excellent. I have gone through and there are very useful pointers. The Plot Digitalizer tool seems to be to very useful. I will check it out today.

Hi pierreick,

Thanks for the article I am going through it now.

Thanks and Regards,
Pavan Kumar

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

Any vendor will give you a pump curve after testing so long as you pay for it....

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Hi LittleInch,

what I was saying that if you take it ( the affinity laws) too far, then other factors come into play which makes the calculation result less and less accurate. SO in your case - 31%, your accuracy is likely to be 10-15%. But you don't need it if you've got a pump curve...

So an example. on your pump curve at say 2000 gpm that's 40 ft diff head. Extrapolating up to 13.5, that's a flow of 2620 GPM and head of 68 ft. The pump curve says at 2620 at 13.5" the head is about 75ft. So a difference of ~10%. Not bad, but not super accurate either.

Based on the link that 1503-44 gave me, the pump curve for impeller size change has to be plotted with the closet impeller. In my case the using Affinity laws to plot the pump curve for 13.5" from the pump curve of 10.3" impeller would be erroneous. I have to use the pump curve close to 13.5" if it is possible to get else ask the vendor for the pump curve. In this case I did ask the vendor. The affinity laws are more accurate for the speed change it appears as geometric similarity is maintained

The pump curve that is generated by the vendor before purchase is a "generic" curve or set of data that they adjust to match your duty point. The actual pump you get has a tolerance of usually 3-5% and still be within validity. Agreed.

VFDs suck about 8% of the power that goes in as heat. So if your motor needs / uses 100kW, the electrical input into the VFD will be about 108kW.

In your example calc 1.1 x 68.7 HP = 75.57. I don't know how you got the answer to be 69.8....

Yes that was a mistake. Instead of multiplying by 1.1 I actually added 1.1 to 68.7!!!.

I think the efficiency changes a bit with speed, but better to ask the vendor of a set of curves at your min, normal and max speeds.

Again per 1503-44's link it appears when the speed is changed the pump efficiency is retained. With impeller size change the efficiency changes depending on how much the impeller size change is.

Don't forget the head falls as a square, so you would only have ~35ft head at 1200 rpm so you would be flowing at about 2000 gpm based on your system curve. Yes 100%. We will use only those speeds that meet our head and flows that fall on our system curve.

Thanks and Regards,
Pavan Kumar

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Hi Littleinch,

Per my calc for 13.5" impeller at full load the pump shaft power = 68.7 HP.

From the motor data sheet I see that at 100% load, the motor efficiency and PF are

nm = 0.95
PF= 0.82

So the power required by motor = 68.7/(0.95*0.82) = 88.18 HP

Adding the 10% losses for VFD, the total power draw would = 1.10*88.18 = 97 HP

My question do you apply 10% power loss on VFD on the motor power draw or the pump shaft power?. In the above thread you calculated total power draw = 1.1*68.7 = 75.57 HP.

Thanks and Regards,
Pavan Kumar

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

On top of the motor power draw.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

Yes, you have pay to get the actual curves for your specific pump.
And if you want anything closer you need to do that

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

Depending on your usage compare using VFD to using a control valve.

Once you add on the VFD losses you might be surprised as to which is more efficient.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Hi All,

Thanks for your suggestions I will now finish my calculations and prepare my comparizon for various options today.

Hi Littleinch,

I will evaluate the option of the control valve too.

Thanks and Regards,
Pavan Kumar

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Thank You Pierre.

Pavan

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Hi All,

Here are the results for the pump options with the various line size options. I am getting the cost of piping ( send piping BOMs to vendors for quotations) for each option further to ROI calculation I will be choosing the line size and hence the operating point.

I have another question. So far a pump that is spare( North Tepid Pump) to this pump under question( South Tepid Pump the vendor gave me the efficiency vs. flow rate curve that is attached. This is the typical inverse parabolic curve I expected as opposed to the iso-efficiency curves given for the South Tepid Pump. My question is that why don't the vendors always give the inverse parabolic curves and instead give the iso-efficiency curves which are harder to digitalize and use in automated spreadsheet calculations. What are the differences between the two. I was told earlier in this thread the efficiency varies the pump impeller diameter, head. Here ( for the inverse parabolic curve) the efficiency varies with only flow rate. Need better understanding.

North Tepid Pump Curve

South Tepid Pump Curve

Thanks and Regards,
Pavan Kumar

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

Hi Pavan Kumar,

The North Tepid pump curve shows the efficiency curve for a 12.25 inch impeller only, where as the graph for South Tepid Pump shows iso efficiency lines in the head - flow field for all impeller diameters.

If you would draw the 12.25 inch impeller head - flow curve in the South Tepid Pump curve, you could read efficiency values per flow rate there from the drawn curve.

The Pump Vendor would gladly provide you desired pump curve, though it will be indicative, as only the test curve gives final data.

Most larger pump manufacturers have selection software allowing Buyers/Engineers to make such curves. Normally representatives or Vendors have to grant you access. Cannot check the types of curves possible with the Goulds software, as I am on my holiday location without access my normal means.

Hope this helps.

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

(OP)
Hi FMJalink,

If I understood you correctly, the pump vendor can provide me the efficiency vs. flow rate curve for each impeller from their software if I request correct?. I will check if I can access / get access to their pump curve software to print the curves myself ( even if indicative).

Thanks and Regards,
Pavan Kumar

### RE: Understanding Centrifugal Pumps Efficiency vs. Flow Rate Curves

Hi Pavan Kumar,
Correct,the Vendor can provide you the indicative efficiency curve for each impeller diameter.
With the selection software of most larger pump manufacturers one can select also the diameter and get the indicative pump curve. I do not remember for sure, whether this also shows the efficiency curve with the Goulds selection software.
Just ask your Vendor or the local pump representative.
Regards,
FMJalink

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