If the flash duration (I think P90 is appropriate), is around 1000 microseconds (1 millisecond, which is shorter than the 540 at full or half power), a falling water drop that has fallen ~0.4 meters will be smeared by about 3 mm - or about the size of the drop! For a flash duration (P90) of around 100 microseconds, the smearing will be 10 times less - but still about 10% of the drop size. I think this is only marginally acceptable. This means that the Pentax AF-540-FGZ must be operated at the lowest powers (1/32 or 1/64) for water drop photography, and that the Neewer flash is marginally acceptable.

However, the conditions are more relaxed: the water drop splashes and collisions are not photographed while the drop is in its original fall.  Rather, the photos are taken of the rebounding water drop.  The rebounding drop rises just a few centimeters, and the same equations of motion indicate maximum speeds of around 0.5 meters per second or less (and pretty close to zero if you catch a drop at the top of its rebound!).  So, the timing requirement is relaxed by almost a factor of 10 - so flash durations at or under 1/1000 second may well be satisfactory for water drop and water drop collision photography.  Of course, the speeds within the splash petal of a water drop collision may be faster.  Clearly, as we say in science, "We need more data!"

I have already taken numerous water drop exposures with the Neewer flashes, and they, in fact, seem quite OK.  Below are some of my best results so far. (These pictures are actually time exposures of more than half a second in length. They were taken in a darkened room, where the flash, when fired, provided essentially all the light.)