So, I just spent the afternoon putting up our outdoor holiday

decorations. So, I figured I should do the same here.

Some of you may recall one of my previous discussions where I

pointed how the interaction

of a centrifugal load like a pump or fan needs to be considered in

the context of the rated motor speed for the motor serving it.

For example, the following table illustrates what happens if a pump

that is rated for a given operating condition at 1,750 rpm is

connected to three different motors, each of which as a different

rated speed at full load.

The bottom line is as follows. Since;

and thus the horsepowerThe torque

generated by an induction motor is a function of its slip – the

difference between its rotor speed and the speed of the synchronous

field in the stator – and,

extracted from a motor by aThe work

centrifugal machine like a pump is a function of the cube of it’s

speed, then

, there will only be one speed where the bhpFor a given pump attached to a given

motor

extracted by the pump will exactly balance the HP generated by the

motor.

My recent insight regarding all of this was that if you obtain

the speed vs. load data for the motor you are considering and then

plot the speed vs. bhp required for the pump you are considering on

the same set of axis, then the point where the two curves cross is

the balance point. In other words, you can develop a graphic

solution to the problem vs. an algebraic solution. The graph below

illustrates this for the three motors and pump associated with the

preceding table.

I like graphic solutions because they let you see your answer in

a broader perspective (plus they may be a bit more user-friendly if

you are math-phobic). If I solved this problem by setting

simultaneous equations, one for the pump power vs. speed and one

for the motor power vs. speed equal to each other a couple of

things come up.

For one thing, I have to develop the equations in the first

place. An exact solution for the motor speed vs. power equation

would involve deriving a polynomial that described the actual

relationship as depicted in the manufacturer’s data. Of course

there are tolerances associated with the manufacturer’s data, so

it’s probably reasonable (but not exact) to assume that the pump

speed to power relationship is linear.

In a similar vein, for the pump, an exact solution would involve

picking flow, head and efficiency points off of the pump

performance curve, calculating brake horsepower from the pump power

equation, and then developing a polynomial that described the line.

Or, I could assume that the pump speed vs. power relationship

follows the affinity laws, a reasonable assumption but not

exact.

Either way, I end up with two equations that contain some

assumptions that can be solved simultaneously for a specific

number. And, I probably had to draw a graph to develop the

polynomial anyway. By simply plotting both curves on the same axis

and looking at where they intersect, I can get the answer I am

looking for with less effort. And, I view it in the context

of the entire power vs. speed spectrum.

In the next post, we’ll look at some resources that will allow

you to get the data you need to do the graphic analysis.