The product of pressure x area, therefore, calculates a force. The K factor is intended to adjust that force to the actual radial thrust. The absence of specific gravity in the equation indicates that its use was intended only for cool water. Although the Stepanoff data was precise and detailed, it reported thrust characteristics for only one size pump.

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I would only use this formula as a rule of thumb. To be accurate, you should have input from the pump manufacturer on this subject with regard to shaft torque and hp limits. There may also be frame limits and occasionally rare impeller blade load torque limits.

Depending on the pump size and impeller geometry, the viscosity limits for the average centrifugal pump will vary from to centipoise, and I have witnessed many pumps successfully pumping fluids in excess of centipoise.

The two important points to take into consideration are these: There is a torque and hp limit for the pump shaft that will be negatively impacted with an increase in viscosity. Make sure to check this viscosity correction factor to ensure a satisfactory and reliable installation. You may still be able to pump the highly viscous fluid with the centrifugal pump, but there will be a point of diminishing returns due to reduced efficiency.

Perhaps you are using 25 hp to pump the viscous fluid with a centrifugal pump that would only require 5 hp with a positive displacement pump. In the case of single stage pumps many manufacturers will express this as a hp per revolutions per minute rpm limit. Note that torque is inversely proportional to horsepower, so the lower the speed the more torque is applied to the shaft. While most shaft limits are based on speed, hp and continuous torque limits, keep in mind that if the pump is driven by an engine then the limits will be further reduced internal combustion means intermittent in lieu of continuous torque.

Additionally, if the pump shaft is side loaded, as in the case of belt or chain drives, there will be a striking reduction on the shaft limits due to the cyclic bending fatigue factor. Note that for gases, it is the opposite relationship.

For stated viscosities a temperature must also be given, typically 40 and C are standards. Temperature can be an issue in the field because pumps are frequently sized and sold to pump a viscous liquid at some stated temperature, but then the pumps are actually operated at a lower temperature, which yields a higher viscosity and, of course, a higher required hp with less flow and head than desired or promised.

They are two different things. Common vernacular expressions confuse us, as viscosity is more often than not erroneously referred to as a thickness or weight.

Mercury has a high SG 13 , but a low viscosity and many lube oils have a low SG lower than water or less than 1. SG is ratio of the density of a substance—fluid in this case—to the density of a benchmark standard, usually water. Note that since SG is a ratio there are no units. Specific gravity is used in the equation when we are converting to or from dynamic and kinematic viscosities. A simple way to explain the difference is that kinematic viscosities are timed flow rates through orifices where the driving force is typically gravity, while dynamic viscosity is a measurement of the force required to overcome fluid resistance to flow through a tube capillary.

Simply put, kinematic is a measurement of time and dynamic is a measurement of force. Before applying the rules, convert to the corrected performance for all applicable parameters. If you are calculating a system head resistance curve and the fluid is viscous you must take that into consideration.

On pump suction line applications where highly viscous fluids have issues flowing in the pipe to the pump suction come to mind, but these issues would normally be covered in the friction component of the NPSHA calculation. That is, the friction factor would be higher for the viscous fluid and consequently reduce the NPSHA. My advice on viscous fluids is to increase the margin between available and required NPSH. With increased viscosity the friction goes up, which results in an increase of NPSH3.

At the same time, higher viscosity results in a decrease of air and vapor particle diffusion in the liquid. This slows down the speed of bubble growth and there is also a thermodynamic effect, which leads to some decrease of NPSH3. This question comes up frequently in my work, and I have researched extensively for an answer but no actual testing. The answer appears to be that at zero flow rate the head developed by the pump is the same for water as it is for a viscous fluid where we assume the viscosity is less than centipoise.

Several of my respected mentors seem to think the same thing. I am open to input if you have data either way. I still would like to believe that a pump of mid- to low-specific speed that is pumping a fluid of mid-range viscosity approximately centipoise will not quite make the same head that it would with water.

But, I surmise that velocity and gravity will argue with me on that issue. Conclusion It is extremely important to know the actual viscosity of the pumped fluid. I frequently witness pump issues in the field due to differences in perceived versus actual viscosity values. Jim Elsey is a mechanical engineer who has focused on rotating equipment design and applications for the military and several large original equipment manufacturers for 43 years in most industrial markets around the world.

He is the general manager for Summit Pump Inc. Elsey may be reached at jim summitpump.

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## ISBN 13: 9780894647239

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## Centrifugal and axial flow pumps

I would only use this formula as a rule of thumb. To be accurate, you should have input from the pump manufacturer on this subject with regard to shaft torque and hp limits. There may also be frame limits and occasionally rare impeller blade load torque limits. Depending on the pump size and impeller geometry, the viscosity limits for the average centrifugal pump will vary from to centipoise, and I have witnessed many pumps successfully pumping fluids in excess of centipoise.

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## Centrifugal and Axial Flow Pumps by A J Stepanoff

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## Centrifugal and Axial Flow Pumps: Theory, Design, and Application

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