Speed-torque curve

A driver (motor, engine, or turbine) must develop sufficient torque to rotate a pump
rotor and accelerate it to its rated speed. The required torque can be calculated
from the formula:

5250 x BHP
T =  ---------------
N
where:

T         -  torque, in foot-pound
BHP   -  brake horsepower required at pump speed
N        -  speed of rotation, in RPM
5250  -  numerical constant to convert torque to foot-pound

Since a driver must develop adequate torque from zero to rated speed, a speed-
torque should be plotted where the percent of speed is shown in the x-axis versus
the required torque in the y-axis.

From
affinity laws we know that BHP varies in direct proportion with the cube of the
speed ratio. Since torque varies in direct proportion with the inverse of the speed,
then the torque varies in direct proportion with the square of speed ratio.

The following tabulated ratio can be used to plot a speed-torque curve:

Speed        Torque
100%          x  1.0
75%            x   0.5625
50%            x   0.25
25%            x   0.0625
10%            x   0.015
0%              x   0.05

This table applies only to centrifugal-type pumps; it does not apply to positive
displacement pumps.

The required torque from zero to 10% speed deviate from the square ratio rule,
and are based on estimates of the frictional or breakaway torque expected from a
pump when starting at rest.

Because the BHP of a pump changes from its zero capacity to its run out capacity,
it is customary to prepare two sets of speed-torque curve - one based on the BHP
at zero capacity (closed valve), and another based on the BHP at the run out
capacity (open-valve.) The run out capacity is customarily set at 125% of the
pump's best efficiency point (
BEP).
Illustration of  typical speed-torque curves depending on the type of pump. For  mixed flow
pump the same curve is shown for both close valve and open valve.  However, this is more
of an exception, rather than the rule. Because there is a large amount of overlap where a
centrifugal pump transitions into a mixed flow pump, and a mixed flow pump into an axial
flow pump, and vice-versa, a mixed flow pump could have a speed torque curve that will
closely resemble that of either a centrifugal pump, or an axial flow pump.
Example of speed-torque curve
Questions:

1. The BHP shown on above [ * ] curve, rated at 7900 RPM, does not go all the way
to zero flow. What  are the reasons for not showing the BHP down to zero flow?
What value of BHP should be used in calculating the torque at close valve?

2. The BHP shown on above [ ** ] curve rises continuously to BEP and then
droops down at run out flow. What BHP should be used in calculating the torque
at open valve - the maximum BHP on the curve, or the BHP at run out?

3.  The BHP on the same [ ** ] curve runs out at about 130% of its BEP.  Most
curves run out at 125% of BEP, others at 120%. At what percentage of BEP should
the BHP be taken in calculating the torque at open valve?

The answers to these questions are available by request only.

R: 0811-SPTO
C: design, operation
F: speed torque curve

Beta version

[ * ] Some information are excluded in this article.