Volume 1
WATER TREATMENT MATHEMATICS
METHODS AND CALCULATION EXAMPLES
Modular Section 4 - Excerpt
Dosage Calculations
Evaluation Sample
SKILL DEVELOPMENT SERIES FOR WATER TREATMENT PLANT OPERATORS
Copyright 2009 Yale Engineering LLC and Sparrow Technical Services LLC
Section 4 - Dosage Equations
Chemical feed in pounds per day = MGD x feed rate, mg/l x 100 % x 8.34 lbs/MG
of chemical
mg/l
8.34 lbs/MG
Chemical feed in gallons per day = MGD x feed rate, mg/l x 100 % x
mg/l
purity of chemical, % x chemical weight, lbs/gal
Pounds of Chemical Fed = Treated Volume, MG x feed rate, mg/l x 100 % x 8.34 lbs/MG
purity of chemical, %
mg/l
Feed mg/l*
Dose, lbs/day x % purity =
MGD x 8.34 lbs/MG x 100%
mg/l
Chemical Feed Pump Setting, % stroke =
Chemical Feed Pump Setting, ml/min =
Volume, gal x % purity x Dose, lbs/gal
MG x 8.34 lbs/MG x 100 %
mg/l
Desired Flow (100%)
Maximum Flow
lbs/gal = pounds per gallon
GPD = gallons per day
% purity
gpm = gallons per minute
C = Concentration
V = Volume
ml = milliliters
L = liters
L/gal = liters per gallon
min/day = minutes per day
ml/min = milliliters per minute
gal = gallons
lbs = pounds
% = percent
SG = specific gravity
ppm = parts per million
MGD = million gallons per day
MG = million gallons
* Dosage ppm = Dosage mg/l
Flow, MGD x Dose, mg/l x 3.785 l/gal x 1,000,000, gal/MG
Chemical, mg/ml x 24 hr/day x 60 min/hr
Copyright 2009 Yale Engineering LLC and Sparrow Technical Services LLC
Section 4: Chemical Dosages
Now that we understand solutions, it is necessary to be able to determine how much of the solution or chemical
must be added to a volume or flow of water to provide treatment at the required level. Dosage equations required
knowledge of the concentration of the solution and the volume to be treated. As a result, intermediate calculation
steps may be required to calculate information required by dosage formulas. Therefore, your previous work on
volumes and solutions may come into play.
Dry chemical dosage or feed rate
Chemical feed in pounds per day = MGD x 8.34 lbs/MG x feed rate, mg/l x 100%
mg/l x % purity of chemical
Dry Chemical
Dose lbs/day
Feed in mg/l
Note that units given in a problem narrative (e.g. ppm, gpm) must be
converted to the units in the equation.
Purity %
Flow in MGD
The amount of chemical that is used each day or other period of time is dependent on the volume of water that is
treated, the feed rate and the purity of the chemical. In the equation above, the calculation of total chemical used is
for a day based on a given flow in million gallons per day. The rate at which chemical is fed into the system is
expressed in mg/l. The purity of the chemical expressed as percent is also used to adjust for the percentage of
actual chemical in the feed. The equation must be multiplied by 100% to convert percentage to a decimal. The
conversion factor 8.34 lbs/MG is used to convert the answer to the correct terms of lbs/day.
mg/l
Copyright 2009 Yale Engineering LLC and Sparrow Technical Services LLC
Equation
Chemical Dosage or Feed lbs/day) = Flow, MGD x Dose , mg/l x 8.34 lbs/MG
purity in decimal form
mg/l
(granular dry chemical )
Typical Problem Statement
Data/Unit Conversions/Calculations
800 gpm
Water flow through a basin is 800 gpm. A
chemical of 30% purity is to be added to the flow
at a dosage of 3 mg/l. What is the chemical feed
rate required in lbs per day?
3 mg/l dosage
800 gal/min x 1440 min/day = 1,152,000 gal/day
1,152,000 gal/day
1,000,000 gal/MG
30% purity
30 % 100 % = 0.30
= 1.152 MGD
1.152 MGD
3 mg/l dosage
0.30 purity
Pictorial
Dry Chemical
Chem. Feed (lbs/day) =
1.152 MG/day x 3 mg/l x 8.34 lbs/MG
0.30
mg/l
3 mg/l
dosage
Flow = 800 gpm
Dosage = 96.08 lbs/day
1 hr = 60 minutes
1 day = 1440 minutes
Chemical feed in lbs/day?
Copyright 2009 Yale Engineering LLC and Sparrow Technical Services LLC
Chemical Feed Pump Settings
Chemical feed pumps are often used to apply the required chemical dosage. As a result, the operator must adjust
the feed settings on the feed pump to dose the chemical at the required rate. A sample calculation to determine the
feed pump settings is indicated below.
Chemical Feed Pump Setting ml/min =
Flow MGD x Dose mg/l x 3.785 l/gal x 1,000,000 gal/MG
Chemical mg/ml x 24 hr/day x 60 min/hr
Chemical
Feed Pump
Other adjustments may be necessary depending on the type
of chemical feed pump used. For example, once the feed
rate is determined, the operator would need to determine
what percentage of the feeders stroke range must be used
to feed at the desired rate. The equation below would be
used for that purpose. For example ,if the feed pumps
maximum output was 100 ml/min and the desired rate was
60 ml/min, a stroke of 60% would be indicated.
Liquid Chemical
Feed
Chem.
mg/ml
Dosage mg/l
Flow MGD
Chemical Feed Pump Setting, % stroke
Desired Flow x 100%
Maximum Flow
Copyright 2009 Yale Engineering LLC and Sparrow Technical Services LLC
Equation
Chemical Feed Pump Setting, ml/min =
Flow, MGD x Dose, mg/l x 3.785 l/gal x 1,000,000 gal/MG
Chemical, mg/ml x 24 hr/day x 60 min/hr
Data/Unit Conversions/Calculations
Typical Problem Statement
Flow = .9 MGD
A water treatment process requires a chemical
dosage of 3.0 mg/l . The chemical has purity of
10% and the flow to be treated is 0.9 MGD. What
is the required chemical feed pump setting in
ml/min? What is the % stroke setting on the
chemical feed pump if the maximum feed rate of
the pump is 5 liters/hr.?
0.5 liters/hr max.
5 liters/hr 1000 ml/l = 83.3 ml/min = max
60 min/hr
.10 = 100,000 mg/l
1000 ml/l
= 100 mg/ml
3.0 mg/l dosage
10 mg/ml
chemical
feed pump
Liquid Chemical
Feed max = 6.0
liters/hour
Dosage =
3.0 mg/l
Chem.
10%
purity
mg/ml =?
10% purity
10 % 100% = 0.10
0.9 MGD
Pictorial
3.0 mg/l dosage
Flow = 0.9 MGD
Feed, ml/min) = ?
Stroke , % = ?
Chem. Feed , ml/min = 0.9 MG/day x 3.0 mg/l x 3.785 l/gal x 1,000,000 gal/MG
100 mg/ml x 24 hr/day x 60 min/hr
Chemical Feed = 70.96 ml/min
% stroke = 70.96 l/min
83.3 l/min
x 100 %
Copyright 2009 Yale Engineering LLC and Sparrow Technical Services LLC
Stroke = 85%
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