can be one of the most intriguing
subjects of photography
must have been speaking of this property with his famous quote You cannot step twice into the same river.
It is equally true that you will never take the same picture of flowing water.
At different shutter speeds, flowing water shows drastically different properties. At very quick speeds, a photograph of water seems 'frozen' as if it was a sheet of glass has been poured over the rocks. A quick photograph of running water from a faucet can show individual drops.
With a long exposure a stream becomes a cloud-like mist flowing over branches and down rocks. Individual waves and ripples become ghostly.
Capturing both extremes of images can only be done on a good 'real film' camera where the photographer has a reasonable amount of control over the camera. Point and click cameras and APS cameras will not fill the role.
The key to the extremes is the amount of light going through the lens and exposing the film. With the aperture wide open, zoomed all the way out or widest angle (this assumes a variable appture zoom lens) large amounts of light will hit the film and thus the quickest shutter speed will be necessary. A side-effect of the aperture wide open (low f-stop) is that depth of field is at its smallest value. This means that objects outside of the water will likely be out of focus.
The other extreme is to let as little light on the film thus keeping the shutter open as long as possible. This is often best accomplished with using a slow film (100 ASA or lower) and possibly with a neutral density filter (such as a polarizing filter) to reduce the amount of light again. This also has the added advantage that slow film has very small grains and is wonderful for enlargements. To again decrease the amount of light hitting the film reduce the aperture (high f-stop) or zoom in. With a high f-stop, the depth of field will be very large (a pinhole camera has infinite depth of field) and most everything will be in focus. Exposure time can eaisly get up to 30 seconds and a tripod will be necessary.
The most interesting fact about both of these extremes of photography is that they capture images that our eyes can never see. We can't freeze a fraction of a second and see that or let a single image be a blurring of almost a minute. We always see in the now.