How do I determine the minimum time to run my filter daily?

How long do I run my filter to turn over the pool water one time? My manual doesn't say.

Under "Specifications", it states that the design flow rate is 44 GPM. If I take my volume (26,000) divided by the GPM (44), I get 591 minutes, or almost 10 hours. Is this right?

Here's my pool stats:

26,000, in ground, steel sided vinyl lined
Hayward S-200 sand filter with Zeolite filter media
CC 3pp
FC 0 :-)
PH 7.4
ALK 150 (I've been told this isn't a problem unless I can't keep my ph down, and my ph holds fairly stable.)
CYA 30 ppm
Temp 84

My power bill is through the roof! We have been running our filter and booster pump quite a bit during the hot days to raise our water temp (we use a country-hick solar system - loose loops of black hose laying on the top of our roof. No home-owners covenants here:-)) But with a pool temp of 84 degrees, I think we can stop running it so much.

Thanks for your help!

P.S. Since the forum history is lost, I want to share for those who were so involved with my two major problems last year (pressure readings and the skimmer lid "geysering" off when I turn off the pumps), both problems have resolved. Our guage was really broke this spring, so it was probably broke last year as well. Replaced it and is now fine. We tightened up our hoses and are keeping the water level a bit higher, and no more geyser.