Blender moving water texture

[Statyk]

The key is trying to keep the UV map as flat vertically as possible (assuming the direction your material is animating. In this example, we will have the material flow negatively, and the water will stream DOWN). This will have the material bend and follow vertexes accordingly. If your UV map is bent like the stream, the water will constantly flow in one direction rather than around bends. Refer to this image while I explain their labels:

Spoiler below!

The Blue arrow shows which way the material will be moving. Downstream of course. The highlighted red squares correspond to each other via model/UV map, so you can see how it will flow. Highlighted YELLOW, is our example of a "faster stream". With the UV short and the model face long, The UV distance must be made up for the length of the model face. This means that the lengthened face will have a faster stream. This will help you with realism when it comes to sharper drops, or if the surface is flatter, make the UV longer than the model face. This does the opposite of the yellow labeled face. Also note that if the water texture is low resolution, simply select all of the UVs of said model and expand them larger. If you look at my UV layout, it surpasses the Quadrant I boundary, so the water material will be repeated more throughout the model, and the material/texture will be of sharper resolution. Don't make it TOO large though or it may begin to not look like water. =P

Hope this helps!

PS, note that the more edges you have on a bend, the smoother and more natural the water flow will look!