Surge tanks vs. rain barrels II

In this post I'm trying to estimate the usefulness of a rain barrel operated as surge tank. 

The valve is open all the time when a rain barrel is used as a surge tank.

This is a bit stream-of-consciousness, and engineering-estimate-like so just skip it if that bothers you.  It could very well be wrong too.  I'm not paid in anything other than pride for this writing gig, so fact cross-checking sometimes gets short shrift.  A little Googling provided the information used herein, and I'm sure you can find similar numbers for your area if you care to.

The first question I asked was how big must a surge tank be to capture rainfall effectively in a downpour?


 
Let's take the maximum rate of rainfall in the Los Angeles area as 2.0 inches/hour (This is the 100 year expectation for our area. The 1 in 10 year rainfall rate for Los Angeles is about 1 inch per hour.)
Assume a 55 gal surge tank.
We'll assume 2.5' of head pressure for the water which is equal to about 1 psi at the spigot (0.43 psi per ft of water).  This will be higher when the water level in the barrel is higher and lower when the water is lower.
The flow rate of a 100' garden hose of 5/8" diameter at 1 psi we take to be 2 gal/min. This is dependent upon the head pressure.

Let's assume 600 sq ft of roof area.  (Given this roof area, with 0.147" of rain you could fill a 55 gallon rain barrel completely.)

In the above situation, 2.0 inches per hour of rain is about 12.5 gallons per minute from 600 sq. ft. of roof.  We can drain 2 gal per minute, which means that we accumulate at 10.5 gal./min.  The 55 gallon surge tank will be full to overflowing in about 5 minutes.  However, this is probably the least of your worries if we get this high rate of rainfall for a prolonged period of time.  The 10 year storm of 1" / hour will fills the 55 gal. surge tank in 13 minutes.

Conclusion: Given the assumptions herein, 55 gallon surge tanks (the size of the most common rain barrel) are nearly useless, even as surge tanks, for 100 year and 10 year storms though they will handle short cloudbursts.

All is not lost, however.  More realistic rainfall rates for our typical storms are significantly less than 1" per hour and at a sustained rate of about 0.32" per hour of rainfall, we can stay even with rain accumulation using our 5/8" garden hose.  That is, 2 gal/minute flows in and 2 gal/min flows out. 

But wait!  If inflow is equal to outflow, then the size of the surge tank doesn't come into play, right?  Right!  The only result that depends upon the size of the tank is the time to overflow.  So, if you don't mind overflowing your tank more quickly during high rates of rainfall, you could have a 5 gallon surge tank.  5 gallons is the volume contained in a 4" i.d. pipe that is 8' long.  You could hide one of these more easily in your garden - perhaps as part of a patio column.  Sure it fills up more quickly - a rainfall rate of only 0.37" / min.hour for 15 minutes would fill it, but since it's taller than the typical 55 gallon rain barrel, the pressure head would be greater when it's full, which would drive a greater flow out of the tank (the assumption of 2 gal/min flow rate through the garden hose could be increased) so you'd get a little relief from over-filling that's not counted in this simple analysis.

So how many storms does a surge tank of 5 gal. capacity handle in a typical rain season?

For that, I have to look at rainfall intensity.  LA County publishes a hydrology manual that is useful in this regard.  Perhaps that will be the subject of a future post.