FILTERATION EFFICIENCY

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FORMULAS FOR PROGRESSIVE
DILUTION (FILTRATION)
OF SWIMMING POOL WATER

The dilution formulas derived and the terminology used by this writer are listed at the end of this report for easy reference. The following examples will show how these formulas may be put to use.

If we have water of a given clarity and without any added dirt load, Formula I will indicate the theoretical clarity in Bits/Gallon (or JTU) at the end of one 24 hour period.

For example, take 24, 000 gallons of water at 1.0 Bits/Gallon and a filter of 50% efficiency flowing at 50 gallons per minute. The water clarity at the end of 24 hours assuming no additional dirt entering the pool is shown as follows:

(1.0 Bit/Gallon)(.2231) = .2231 Bits/Gallon at end of 24 Hours

 If we take this same example and assume some average amount of continuous Hourly or Daily dirt addition we will find that the pool clarity will stabilize at a         certain level regardless of the starting condition of the water. Formula II gives:

Which is abbreviated as Z, the time period dilution factor, in this case 24 hours.

Taking a daily dirt addition of 1.0 Bits/Gallon the pool clarity will reach equilibrium or stabilize at

We could take the same example and calculate it on an hourly basis as follows:

 

Dividing the dirt load over 24 Hours gives:

Using Formula II to calculate the point of pool clarity equilibrium we have:

 This shows that dirt added more or less continuously (hourly) has a more serious effect on pool water clarity than the same quantity added once daily (prior example).

Formula III more accurately depicts swimming pool operation - daytime bathing loading with a reduced 24 hour environmental loading. Again the foregoing example will serve as a basis for this example with the following modifications.

Let us assume the 1 Bit/Gallon per 24 hour dirt loading is divided .8 Bits during 8 hours of pool usage and .2 Bits during the 16 hours of nonusage, giving .1 Bit/Gallon/Hour = DL, and .0125 Bits/Gallon/Hour = NL.

From Formula III solving for Y first:

Then Formula III

Pool clarity at end of 8 hour bathing period.

To get the theoretical pool clarity at the end of the 16 hour cleaning cycle we use Formula IIIa

(.880)(.5069) = .447 Bits/Gallon pool clarity at end of 16 hour cleaning cycle.

These figures represent the clarity levels after several days of operation under these conditions.

One final condition of pool operation perhaps should be considered and that is one of time clock shut down during some of the hours of non use. Keeping with the foregoing example, we have but two changes to effect. First for simplicity we consider the dirt load during the hours of non use to fall during the remaining hours of filter operation; and second we adjust the term "n" to accurately reflect the hours of filter operation remaining during the non use period of the day.

For example if we turned our filter off for 10 hours each night we would have

and

Substituting these figures in Formula III

Pool clarity at end of 8 hour loading period.

And (1.21)(.820) = .996 Bits/Gallon at end of 6 hour cleaning cycle.

A rapid comparison can be drawn here between .88 and 1.21 for the clarities at the end of loading and .50 and .99 at the end of the cleaning cycle due to the reduced cleaning cycle time. Potentially a material effect on pool water clarity in pools of high dirt load levels. However, in practice - particularly residential pools and off season public pools - dirt levels are generally considerably below filter capacities and on off operation can be practical. Whenever load conditions demand, the system can be left on continuously and the benefits of full time filter operation can again be realized.

This work is based upon the theoretical aspects of swimming pool filtration and is only intended to serve as somewhat of a guide in projecting and understanding actual performance - obviously additional factors can come into play from one installation to another.

Results in these examples were rounded for convenience, however, fuller numbers were used in the subsequent calculations creating more accurate answers that vary slightly from the rounded number computations.

Reference Sheet I

FORMULAS & TERMINOLOGY

Dilution Formula (I)

Progressive Dilution Formula (II)

Reference Sheet 2

FORMULAS & TERMINOLOGY (Cont'd)

Cycle Progressive Dilution Formula (III)

Cleaning Cycle Formula IIIa

"Bit" is the term used to describe a quantity of turbidity.

1 Bit is the quantity of Turbidity represented by a level of 1.0 Jackson Turbidity Units in 1 Gallon of water.

When the term is expressed as "Bits/Gallon" it is synonymous with the expression "JTU"