The volume of water in a rectangular pool is the product of width, height and average depth. For your pool that would be
20 * 40 * (3.5 + 5.5)/2 = 3600 cubic feet
3600 cubic feet * 7.48051945 gallons/cubic-foot = 26,930
or about 27,000 gallons.
The above calculation assumes that the average depth is the average of the shallow and deep end depths. This is reasonable when the area of the shallow and deep ends is roughly the same and that the area of the transition between these two ends is also about that same size (i.e. the pool is roughly in one-third sections of shallow, transition, deep). Every real pool will be a little different.
As for BioGuard Smart Sticks, they are slow-dissolving Trichlor that stop dissolving when there is no water flow so presumably prevent the buildup of acidity that would occur in the skimmer basket when the pump is not running. The problem with Trichlor is that it contains not only chlorine, but also Cyanuric Acid (CYA) and this can build up over time. For every 1 ppm Free Chlorine (FC) introduced by a Smart Stick, you also get 0.6 ppm CYA.
As for whether or not this is a problem in your particular pool, that depends on what kind of filter you have, how often you backwash or have splash-out, whether you have summer rains that overflow and dilute your pool water, etc. Usually in a larger pool such as yours the buildup of CYA will occur. As the CYA level increases, it makes the chlorine less effective so requires a higher FC level to compensate so that you have the same disinfection, oxidiation, and algae prevention capabilities. Ben's Best Guess CYA chart here shows the recommended FC range (Min/Max and Shock levels) for various CYA levels. If you don't use an algaecide regularly, then your pool may develop algae. The BBB method avoids having to use alagecide (at least regularly -- it is often used for closing) and maintaining a pool mostly using chlorine alone and specifically bleach or chlorinating liquid (whichever is less expensive or more convenient) since they do not contain CYA (you need some CYA initially and can even use Trichlor to build it up as needed, but then switch to bleach once your pool has the desired CYA level). See this post for more info on BBB which is mostly about using store-bought chemicals that are equivalent to pool store chemicals (at least when they are less expensive, which is usually the case).
You should invest in a good test kit such as the Taylor K-2006 shown here or the equivalent kit from Leslie's called the Chlorine FAS-DPD Service Test Kit shown here or you can get a similar kit that has more intelligent amounts of reagents in its tests at Trouble Free Test Kits here. All of these test kits will accurately measure Free Chlorine (FC), Combined Chlorine (CC), Total Alkalinity (TA), Calcium Hardness (CH) and Cyanuric Acid (CYA).
Richard
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