Fast / Easy is all based on the skill sets of the individual. Whats easy for one person may not be easy for another so not sure how these suggested methods will rate on the fast/easy scale.
So if you have a straight pipe with no curves/bends…then you could use scale or create a shapekey and animate the shave value.
However if you have curved pipes… the problem can become a tad bit more difficult.
If you pipe has no connectors…more like a bent hose….then you can just use can use a UV map with transparency to run the distance of the pipe. You then assign value to the inputs of the UV map and animate those or drive those with puzzles.
If your pipe has connectors: elbows, T’s, crosses, valves, etc and they are separate objects then you will need a different approach combining UV maps for the complex shapes and scale or shape key or UV maps for the straight parts.
Depending on your situation/needs you could also use a clipping plane .
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