The affinity laws
For a given impeller, flow rises in proportion to speed, pressure (head) rises with the square of speed, and power rises with the cube. Slow a pump down by 20 percent and it needs only about half the power. That relationship is why variable speed drives can save so much energy on irrigation systems that do not always need full flow.
Try it: drag the speed from 1750 to 1400 rpm and watch power drop to roughly half while flow drops by only a fifth.
Why the casing is a spiral
Water leaves the impeller fast all the way around. The volute collects it in a passage that grows steadily larger, so the water slows evenly. Slowing a moving fluid in a widening channel converts its speed into pressure, the same idea that lets a garden hose nozzle trade pressure for speed in reverse.