Velocity triangles

At the airport you walk on a moving walkway. The walkway carries you forward, and you also walk. Someone standing beside it sees you go by at walkway speed + walking speed.

Now walk diagonally across it. Your speed seen from outside is an arrow made by adding two arrows: the walkway’s and yours. That is a velocity triangle.

u — the speed of the vane tip itself, going round (like the walkway). w — the water’s speed as seen by someone riding on the vane: it slides out along the vane (like you walking). This is the relative velocity.

c — the water’s real speed, seen from the casing: c = u + w, added as arrows. This is the absolute velocity.

You are zoomed in on the rim of the impeller, right at the tip of one vane. The impeller turns to the right.

Change the speed, the flow and the vane angle. Watch how the three arrows always close into a triangle.

Speed stretches u. Flow pushes water out faster through the impeller, which lengthens the part of w that points outward.

The vane angle tilts w. Backward-curved vanes tilt w backward, so c ends up shorter than u. Forward-curved vanes tilt it forward, so c is longer than u.

At the eye there is another triangle. For a smooth entry, the leading edge of each vane must point exactly along the incoming w — otherwise the water hits the vane edge sideways and loses energy.

That match is only perfect at one flow: the design flow. It is one reason pumps are happiest near their best efficiency point.