So, I get that voltage is the difference in electrical potential energy per unit charge between two points. However, many textbooks and online resources compare voltage to the height of a waterfall to point out that you need a difference in height to produce a current. That makes sense. What doesn't make sense is why increasing the height (which is supposed to correspond to voltage) would increase the rate of the flow of the water. The water is not leaving the top of the waterfall any faster than before, so why would current increase? I know that the water has more height to fall and its final velocity will be higher because it has more time to accelerate, but wouldn't that just mean the water droplets just get spaced out further apart, so the actual amount of water passing a point per second won't increase? So, why would increasing the difference in how much electric potential energy each coulomb of charge has between two points mean more current will flow between those two points?

Sorry if this is an extremely basic question. I can do circuit analysis and apply Ohm's law, but I am just trying to get a full picture of the intuition behind Ohm's law rather than just accepting it and moving on (the inverse relationship between current and resistance makes perfect sense to me, though, so I'm good with that).

I understand that voltage is the difference in electrical potential energy per unit charge between two points. 

However, many textbooks and online resources compare voltage to the height of a waterfall to illustrate that you need a potential difference a current. What doesn't make sense is why increasing the height   (analogous to increasing voltage) increases the flow rate of water (analogue to current).

I know that the water has more height to fall and its final velocity will be higher because it has more time to accelerate, but wouldn't that just mean the water droplets just get more spread. Hence, the actual amount of water passing an area per second wouldn't increase? 

So, why would increasing the difference in how much electric potential energy each coulomb of charge has between two points mean more current will flow between those two points?