There are several utility companies that use a similar scheme for storing off hours generated electricity, long term costs are much lower than batteries, and efficiency is greater.
Of course, they generally use a storage lake, and are located in regions that would easily support it.
Calculating the capacity would depend on your hydroelectric setup figured in gallons per minute, and feet of head. There are many resources to figure all that.
Overall, it is an interesting idea, but for most RE'ers I doubt it would be very cost effective over a battery setup, the controls and equipment would be cost prohibitive on a small scale.
Let's say you put up a 1,000 gallon tank, (Huge I'd hate to see the support structure) and you installed a 5 gpm hydro generator on it, you'd have enough capacity to run for 3 1/3 hours. Now how long is it going to take to fill that tank?
If you had the tank 50' elevated,at 5 gpm you'd get a WHOPPING 18 Watts or 13 kwh a month out of it. (That's assuming you can run it 24/7).
Just running some numbers... 3,000.00 for a windmill and tower, probably 4,000.00 for a storage tank(assuming you can't build a pond for storage), add in piping let's say 500.00, then your hydroelectric generator, 2,500.00 So far you've invested over 10,000 or more.(adding in controls and inverters, etc).
That amount would buy you a decently sized photovoltaic system. And the amount of power you'd have would be far greater.
I'm not saying that it wouldn't be feasible in the right circumstances, just not with a water tank, the only way I could see if of benefit is if you had an area high enough to put in a storage pond that could give you a flow rate of at least 2 gpm, and a decent amount of head, and you built the majority of the components yourself.
Remember you're using potential energy to pump the water uphill, then you're generating electricity off the downhill flow, so you've got losses. considering hydroelectric is about 90% efficient, and you also have the loss in pumping.
Some ideas to improve on the scheme, pumping water uphill with a hydro ram, then storing it in a small pond. That would require a surface stream with a gpm flow of 80% over what you wished to store. This is dependent on the height pumped.. Also it would make sense if you had a pre-existing pond that didn't maintain a steady outflow (and you had a separate source for extra water). Then you could upgrade it to hydro.