Toronado is right, axial and radial just refers to the direction of flow with regards to the motion of the device. Axial flows along the same AXIS as the work shaft, radial flows by RADIATING away from it. So from that standpoint there is technically insufficient information to make a determination. But I'm going to have some fun with this based on a class I recently taught on understanding the benefits of VFDs.
GENERALLY there are conventional descriptions of (non-positive displacement) pumps that fall into the two (2-1/2) categories of "Axial" vs "Centrifugal" (what you are calling Radial), and the 1/2 category is actually what's called a "Mixed Flow" pump. The effects of flow restriction are different in those types as you have noted.
Maybe think of it in other terms if it will help.
An Axial Flow pump can be thought of like an airplane propeller. The faster the prop spins, more "stuff" (air or water) it displaces and the more thrust it generates. But if you restrict the flow coming into or out of it you create turbulence, so it becomes more difficult for that prop to work against that turbulence.
So when run at the same speed and the same thrust capability, the motor works harder to overcome the restriction even though the net work being performed (defined as flow) is lower.
Now for a Centrifugal pump, think of one of those push type merry-go-round play structures at the playground. Imagine 20 children loaded up on top of it, all the way out to the edges. Now imagine trying to spin it. It's going to be difficult, right? So imagine an endless flow of children dropping into the center while it is spinning, and the children on the outside edges falling off at the same rate. The work you have to do to in order to keep it spinning is constant right?
Now imagine that the number of children dropping into the center is lower than those being flung off of the edge. In a few minutes, you have less total children in the platen right? The effort you have to exert to keep it spinning is going to be less. that is a Centrifugal pump. Less flow = less work. Restriction means less flow.
A Mixed Flow pump is like a merry-go-round on a moving airplane. Bloody mess.
No wait, a Mixed Flow pump is like a ... well, I can't come up with a good analogy. But it combines both characteristics and acts slightly different depending on the flow, but generally the power requirements are along the lines of a Centrifugal in that flow restriction decreases power requirement, just less dramatically. A lot of pumps that are called Centrifugals, such as sewage lift station pumps, are really mixed flow but because they generally follow the same type of power curve, nobody gets excited about the semantics. But it does mean that some of the dramatic energy savings typically thought of by using VFDs are not going to be quite as dramatic
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