Use Tip speed to estimate Head 1

[billbusy]

Clearly the pump head is relevant with impeller tip speed, I am just wondering if there is a formular to estimate pump head by tip speed? Thanks

Oil & Gas industry in Canada.

 

[ashtree]

You are correct up to a point. For a given pump there is a relationship between impeller tip speed and head. Higher speed will give higher head.
The pump affinity laws show the relationship.

Volume Capacity

q1 / q2 = (n1 / n2) q is flow n is speed or rpm

Head or Pressure

dp1 / dp2 = (n1 / n2)2 dp is discharge head or pressure

Power

P1 / P2 = (n1 / n2)3 P is the power required

However as each style of pump/model/brand has different operating characteristics, different impeller configurations , efficiency , internal leakage from high pressure to low pressure etc , there is no generalised equation of formula linking tip speed to head.

A classic example of this would be a wastewater pump with a very open vortex impeller. The tip speed may be just as high as another pump with a multivaned enclosed impeller. But the vortex type may only be able to achieve 10 m head where as the other may be able to do 50m head.

Regards
Ashtree
"Any water can be made potable if you filter it through enough money"

 

[DubMac]

No sir.

 

[TenPenny]

Somewhere I did read a quick formula to give you a rough estimate of SHUT OFF head bassed on tip speed, or, in the case I recall, diameter and rpm (which amounts to the same thing).

So the short answer is, yes.

 

[TenPenny]

Found it.

Note that this is a way to estimate SHUT OFF head only, and is useful for estimates only. Once flow is developed, there is too much variation with clearances, impeller design, etc etc etc.

But, if you want a way to estimate shut off head:

The maximum or "shut-off" head of a centrifugal pump can be expressed as

hs = (d n / 1840)^2

where

h = head (feet)

d = outside diameter impeller (inches)

n = wheel velocity ( revolution per minute - rpm)

 

[billbusy]

thank you guys. very helpful!!!

I am working with a pump company and they have a software to estimate the rpm (by the tip speed) by the pump head.

It seems they may have some tested data for a better relationship between tip speed and pump head.



Oil & Gas industry in Canada.

 

[electricpete]

The maximum or "shut-off" head of a centrifugal pump can be expressed as

hs = (d n / 1840)^2

I'm guessing that can be deduced from Bernoulli's principle: 0.5*rho*v^2 + rho*g*z + p = constant

assume no change in z.
Assume v = (2*pi*[R])*N = 2*Pi*[D/2)]*N = Pi*D*N for max kinetic energy term at blade tip
Then assume all KE converted at blade tip is converted to pressure energy at the pump outlet for max pressure at pump outlet
Bernoulli tells us:
P = 0.5 * rho * v^2 = 0.5*rho * (Pi*D*N)^2
hd = P/rho = 0.5 * (Pi*D*N)^2

we can see hd ~ (D*N)^2 matches the expression posted above.
With unit conversions I'm guessing it will give the same proportionality constant, but I haven't gone thru the excercize.
See other caveats from TenPenny. Since no losses are considered (recirculation etc) so this shutoff maximum would probably not be attained in practice

=====================================
(2B)+(2B)' ?

 

[DubMac]

I'm really struggling to understand how a radial flow impeller, Francis vane, mixed flow, and propeller pumps with identical tip speeds would all generate the same head. This tortures the definition of "estimate" to its breaking point.

If you were talking about comparing heads of the same impeller with varying tip speeds, then OK; but then you could do the same just using the rpm.

 

[ashtree]

DubMac i am struggling with you on this one.

A pump company that manufactures a particular style of pump may well be able to develop a formula that would estimate shut off head for their pump. Given that so many of the different brands produce pumps that are broadly the same those equations may even have some relevance to several different brands of a similar style. Beyond that i am a skeptic.

Regards
Ashtree
"Any water can be made potable if you filter it through enough money"

 

[ashtree]

I went and dug up a couple of pump specifications and used the formulas above.

On a Grundfos NB(close coupled moderate head pump with a closed impeller) the calculation got me within about 15% of the shut off head but low. Not too bad for a first pass estimate i guess.
I then did the calculation on a Grundfos TP which is a circulator pump which has a semi open impeller. This gave me a grossly incorret result with the calculation being 2.5 times greater than the published shut off head.

I would suggest that the formula if of any use will be for a particular style of pump and not much use for anything else.



Regards
Ashtree
"Any water can be made potable if you filter it through enough money"

 

[TenPenny]

Just for fun, I did a random sampling of some Goulds Pumps, 3196, 3180 (End Suction, open and closed impellers), 3900 (vertical inline API), 3410 (double suction/split case), and VIT vertical turbines.

The formula used as a rough estimate for shutoff gave results that ran from 17 to 21% below what the printed curves show.

It's obvious, however, that it is impossible to use a set formula to relate tip speed to head at anything other than zero flow, because the number of vanes and the impeller design determine the shape/slope of the performance curve.