how to calculate the Pump load curve 1

[760106]

For centrifugal pump,to ensure the motor accelerating the pump to rated speed, the requirement of motor torque should always be higher than the pump load torque.
1. Is there any body know how to calculate the pump load with diffirent rotating speed?
2.normally, pump manuafacture provide us the Motor torque curve and pump load curve. I want to know in which condition these curve is tested. the discharge valve is fully closed or opened during test?
3.and I also want to know if this load curve change with different back pressure in the upstream of the discharge check valve.

 

[cbrn]

Only approximate answers, as calculating the pump's characteristics is a very complex matter:

1- you can do that in analytical way. You have several equations which govern the fluid motion through an energy-adding device (a pump). Any book dealing with turbomachinery has them, and I suggest you to start by that as I fear it would be extremely difficult to write equations here

2- if it is the head-vs-flowrate curve that you are refering to, then it's simple: pump is started with closed valve and the maximum head is measured; then the valve is progressively opened and both flowrate and head are measured; the measured data won't go up to the max flowrate corresponding to the zero head, because of the losses in the test circuit: the curve is then extrapolated.

3- the pump has a minimum imposed energy that the fluid must have at the inlet in order not to have cavitation at the impeller's leading edge: this is called NPSH and installing the pump so that the pressure of the fluid at the inlet is below the NPSH can have dramatic consequences. Making the pump outlet into a pressurized ambient has no negative side, simply the upstream pressure is seen as a circuit load and so the flowrate will decrease following the pump curve. If the discharge pressure is higher than the max pump head, there will be backflow (and this is not good at all... ;-) )

As a way to estimate the starting torque, apply the first equation of dynamics to the rotating mass (inertia) of water encomprised into the runner + the inertia of all the rotating equipment: M=I.alfa.

 

[760106]

cbrn (Mechanical):
thanks for your answer, but I still not satisfied with these.
1.For qestion one, can you recommend me any books that I can find the equation or the analytical procedure?
2. For second question, my question is for the motor torque curve and pump load curve. You know the motor torque curve will be changed with the different open position of discharge valve beacause of the changing of starting time, is it correct? so, I want to know which condition the pump manufacturer considered nomally.
3.the third question, I can explain as following. When two identical pumps installed in parallel, when one pump is running at rated point, can another pump be started with the discharge valve fully open? even the second pump can be started, I want to know if the pump load curve will change with this diffirent back pressure in downstream.

 

[vanstoja]

In my experience, centrifugal pump load-speed torque curves plotted versus motor torque-speed (where speed is usually in percent of synchronous load speed) are usually determined from one point, the measured full-load slip speed (synchronous minus actual speed)intersection with the motor torque curve at rated/design flow and the rest of the load curve down to zero speed is assumed to be a parabola varying with the square of the speed which is representative of a friction-only pipe flow resistance. Rated flow would be controlled by discharge throttle valve setting in the manufacturer's test loop which might be fully or, more likely, partially full-open. This single flowrate test condition won't tell you anything about the punp load torque curve at any other flow conditions. You'd have to test for actual motor speed at other selected flowrates to determine the load torque curves for various non-rated flowrates. Discharge check valves would not likely be installed in a manufacturer's test loop so tests would have to be run in the actual operating plant that might employ check valves for pumps installed in parallel.
Plotted motor torque curves often are "smoothed-out" and don't show actual cusps an other discontinuities at runup speeds below full-load speed so motor hangup at reduced speed (with consequent winding overheating) is a concern when pump load-torque curves get steeper than for rated flow startup conditions.

 

[cbrn]

760106,
1- not easy for me to recommend turbomachinery texts, as the ones I know are... in Italian!

2- IMO vanstoja very well answered this point. I agree that in general the manufacturer would indicate the operating point(s) he is refering to.

3- I see a problem in starting the second pump with the discharge valve fully open: there will be back-flow through this second pump for all the time it takes for it to reach the operating point. In this case it is also possible that the pump would not start at all. Why not start it with discharge valve closed (torque required is less than in fully-open, this is an opposite behaviour as with axial pumps), then open the valve? Sure, you will transitorilly disturb the first pump for a while, and the whole circuit as well, but as centrifugal pumps normally have a stable behaviour (i.e. they have monotonic head-vs-flowrate curve) both pumps will rapidly reach the new equilibrium, with twice the flowrate (if the pumps are identical) as with one pump only, and of course the same head.

 

[760106]

Thanks to vanstoja and cbrn.
After vanstoja's expaination, I understand better than before.
could you tell me how to determine the pump load torque at the full-load slip speed. is it tested with motor or only calculated?
could you tell me the procedure the pump manufacturer purchase the motor. how much information should the pump manufacturer shuld provided to Motor manufacturer?

 

[vanstoja]

Measure motor actual speed in RPM at full load operating conditions , then subtract from synchronous speed (3600, 1800RPM. etc.) and divide by synchronous RPM to get fractional slip speed. With a copy of the motor torque curve with percent speed from zero to 100, measure off percent slip speed back from 100% and draw a vertical line through the descending torque curve. The intersection point is the motor's full load torque value, the starting point for a parabolic load curve extending back to zero torque at zero speed.

 

[bulkhandling]

The formula for torque calculation:

Hp=2x3.14159xNxT/33000

Where Hp: motor brake horse power
N: pump speed, rpm
T: pump torque, lb-ft

 

[Pumpinterest]

vanstoja,
I have checked all the centrifugal pump torqe curve I had ever contacted, most of them just like what you said that the curve is a parabola. But only only fire water pump is different, which was made by FLOWAY Company and required to start with the discharge valve fully open.
The value of pump load curve is very small(about 289Nm) at zero speed;the value of load is zero at very low speed(about 3%full speed); then the pump load is increasing with the speed increasing, at last, the pump load reach to 1637Nm at the full speed. so can you explaine this?