It occurred to me one day that when one doesn't have a neutral density filter and there is too much light to shoot at the longer exposures needed to feather (blur) moving water - for something like waterfalls this is typically anywhere from 1/15 second to several seconds, depending on how much motion blur is wanted - one can instead take several exposures at faster shutter speeds and then stack them later in an image editor (Photoshop in my case).

Image Stacking, also called Image Averaging, is a common practice in astrophotography to reduce image noise and a lot of information about it can be found online, but in essence you take multiple shots of a scene without moving the camera and then copy each shot into its own layer in an image editing file and adjust the opacity of each layer to this formula...

  1 divided by the layer number, counting from the bottom up.

Or in other words, like this for a stack of ten...

Layer 10 - 10% opacity (1 divided by10)
  Layer 9 - 11% opacity (1 divided by 9)
  Layer 8 - 12% opacity (1 divided by 8)
  Layer 7 - 14% opacity (1 divided by 7)
  Layer 6 - 17% opacity (1 divided by 6)
  Layer 5 - 20% opacity (1 divided by 5)
  Layer 4 - 25% opacity (1 divided by 4)
  Layer 3 - 33% opacity (1 divided by 3)
  Layer 2 - 50% opacity (1 divided by 2)
Base layer - 100% opacity (1 divided by 1)

There can be any number of layers in a stack and the more images there are in a stack, the smoother the motion blur will be, but you get diminishing returns with each added layer, so in my experience a practical number is around 8 to 10 layers.

This technique works best if one still uses the slowest shutter speed possible to get as much blur in each image as is possible, even though it’s not enough in each image for a feathered blur.

One caveat with this technique is that you don’t want anything else in the composition to be moving, just the water, because anything else that’s moving will also be blurred.

Another caveat is that the blur produced by this technique is not as smooth as you get from a proper time exposure.

But one benefit of this technique beyond blurring motion is the resulting image noise will be lowered.

It is, of course, best to take multiple shots from a tripod. If you are in a position where this isn’t possible or practical or you simply don’t have a tripod with you, you can take a handheld burst of shots (holding the camera as steady as you can, preferrably bracing against something) and then use the ‘Auto Align Layers’ function in Photoshop to align the stack of layers. This actually works quite well, although not as easily as having used a tripod.

Below are two sets of examples, the first image in each set showing a single shot taken with a shutter speed too fast to effectively blur the water motion, and the second image showing the result of stacking multiple shots.