A centrifugal pump is considered which type because the discharge volume changes with the head?

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The key idea is how the pump's flow responds to system head. Centrifugal pumps are dynamic devices, not fixed-volume machines. They impart velocity and pressure to the fluid, and the actual discharge depends on the head the system presents. When the head increases, the pump’s ability to push fluid slows, so the discharge volume changes with head. That behavior characterizes nonpositive-displacement pumps—the flow is not fixed per revolution but varies with the system conditions.

Positive-displacement pumps, by contrast, deliver a nearly constant volume per cycle regardless of head (within design limits). Rotary-displacement is a subset of positive-displacement pumps, where rotating elements trap and move a fixed amount of fluid each cycle. “Variable-displacement” isn’t a standard category for describing centrifugal behavior.

So, because the discharge changes with head, a centrifugal pump is best described as nonpositive-displacement.