Just to play the devil's advocate here, if you really could simplify the relation between volume and volatility the way you describe, could it not be arbitraged away?
The relationship between volume and price fluctuation/volatility is poorly understood, and is in fact actively debated in trading as well as academic circles AFAIK. There are a few systematic studies in this area but even they are inconclusive or speculative at best, or have been contradicted by more recent studies. 'Stock Prices and Volume' research paper by Gallant, Rossi et al. is a good starting point for those interested in this topic. Old but still gold.
There is a clear correlation between Volatility and Volume.
That's why as an intraday trader I tend to trade event-driven.
Because I know that usually if there is volume, there is volatility.
That means I want play the open or events accompanied with volume.
However I have not found yet that volume helps to forecast prices.
And I know that volume is not the only variable for volatility.
It's only half the equation, the other half being: Liquidity.
But don't mistake Volatility plays for Directional ones.
If you break down volume into orderflow,
Some claim persistence of its sign over a short period of time.
Intraday I've also observed a relation between Volume and Phases.
But it's less empirical and more of an art currently, at this stage.
High vol being the relay from buyers to sellers & vice versa.
I believe there are waves of buying as well as selling.
Volume could shows the transition between them.