11.2 Chemical Dosage, The Standard "Pounds Formula", Active Chemical & Solution Purity
Key Takeaways
- The universal Pounds Formula states: Chemical Feed (lbs/day) = Flow (MGD) × Dosage (mg/L) × 8.34 lbs/gal.
- The constant 8.34 represents the mass of one gallon of water and bridges the metric concentration (mg/L, equivalent to parts per million) to Imperial daily mass units (lbs/day).
- Commercial dry chemicals with active strengths less than 100% require dividing the calculated pure chemical demand by the decimal purity (Commercial lbs = Pure lbs / Purity Decimal).
- Liquid chemical feed calculations must incorporate the solution's Specific Gravity (SG) and percent concentration to determine active chemical mass per gallon: Active lbs/gal = SG × 8.34 × Concentration Decimal.
- To convert liquid feed rates from Gallons per Day (GPD) to laboratory/metering pump milliliters per minute (mL/min), multiply GPD by 3,785 mL/gal and divide by 1,440 min/day (shortcut multiplier: GPD × 2.6285 = mL/min).
Chemical Feed Calculations & The Davidson Pie
Accurate chemical dosing is vital for disinfection, coagulation, pH stabilization, and nutrient removal. Under-dosing fails to achieve pathogen destruction or turbidity reduction, while over-dosing wastes utility funds, risks regulatory violations (such as disinfection byproduct formation), and may create toxic conditions in receiving streams. The standard Pounds Formula (historically taught using the "Davidson Pie" visual mnemonic) serves as the primary tool for calculating chemical addition in water and wastewater systems.
The Fundamental Pounds Formula
The standard formula connects volumetric daily flow, chemical dosage concentration, and the physical density of water:
+-------------------------------------------------------------------------+
| THE DAVIDSON PIE CHART |
+-------------------------------------------------------------------------+
| |
| [ Pounds / Day ] |
| ------------------------ |
| [ Flow ] [ Dose ] [8.34] |
| (MGD) (mg/L) (lbs/gal) |
| |
+-------------------------------------------------------------------------+
Mathematical Proof of the 8.34 Constant
Operators often ask why $8.34$ is the universal constant. It is derived from the conversion between metric concentration and English mass units:
- $1\text{ mg/L} = 1\text{ part per million (ppm)} = \frac{1\text{ lb chemical}}{1,000,000\text{ lbs water}}$
- $1\text{ gallon of water} = 8.34\text{ lbs}$
- Therefore, $1\text{ Million Gallons (MG) of water} = 1,000,000\text{ gal} \times 8.34\text{ lbs/gal} = 8,340,000\text{ lbs of water}$
- Dosing $1\text{ mg/L}$ into $1\text{ MG}$ yields:
Algebraic Variations of the Pounds Formula
Depending on the known and unknown operational variables, the formula can be rearranged:
| Desired Parameter | Manipulated Formula | Operational Application |
|---|---|---|
| Chemical Feed Rate (lbs/day) | $\text{lbs/day} = \text{Flow (MGD)} \times \text{Dose (mg/L)} \times 8.34$ | Setting gas chlorinators, bulk chemical orders |
| Delivered Dose (mg/L) | $\text{Dose (mg/L)} = \frac{\text{lbs/day}}{\text{Flow (MGD)} \times 8.34}$ | Verifying actual dosage from feed scale logs |
| Treated Plant Flow (MGD) | $\text{Flow (MGD)} = \frac{\text{lbs/day}}{\text{Dose (mg/L)} \times 8.34}$ | Calculating capacity treated by known chemical mass |
| Static Tank Batch Dose (lbs) | $\text{lbs} = \text{Volume (MG)} \times \text{Dose (mg/L)} \times 8.34$ | Shock chlorinating a storage tank or basin |
Note for Tank Batch Dosing with Gallons: If tank volume is given in gallons rather than MGD, divide gallons by $1,000,000$:
Adjusting for Chemical Purity & Active Constituent Strength
The standard pounds formula calculates the required weight of 100% pure active chemical (such as pure gaseous chlorine, $Cl_2$). However, many commercial chemicals are shipped as dry compounds or liquid solutions with active strengths significantly below 100%:
- Calcium Hypochlorite (HTH): Dry granular/tablet disinfectant typically contains 65% available chlorine by weight ($0.65$ purity).
- Hydrated Lime ($\text{Ca(OH)}_2$): Commercial lime used for pH/alkalinity adjustment typically possesses 90% purity ($0.90$ purity).
- Soda Ash ($\text{Na}_2\text{CO}_3$): Industrial grade soda ash typically has 98% purity ($0.98$ purity).
To determine the actual pounds of commercial chemical product required to deliver the target dosage, divide the calculated pure pounds by the decimal purity:
Rule of Thumb: Because commercial chemical is never 100% pure, the required weight of commercial chemical will always be greater than the pure active weight calculated by the base pounds formula.
Liquid Chemical Feed Solutions & Specific Gravity
Liquid chemicals—such as sodium hypochlorite ($NaOCl$), liquid alum, ferric chloride, and aqueous ammonia—require accounting for both solution strength (percent active ingredient by weight) and solution density via Specific Gravity (SG).
Specific Gravity & Liquid Solution Weight
Specific Gravity is the ratio of the density of a liquid compared to the density of pure water at $4^\circ\text{C}$ ($1.000\text{ SG} = 8.34\text{ lbs/gal}$):
To calculate the active pounds of chemical contained within one gallon of liquid solution:
+-----------------------------------------------------------------------------------------+
| TYPICAL LIQUID CHEMICAL CHARACTERISTICS |
+-----------------------------------------------------------------------------------------+
| Chemical Solution | Typical Specific Gravity (SG) | Concentration (% by weight) |
+-------------------------+-------------------------------+-------------------------------+
| Sodium Hypochlorite | 1.18 to 1.22 (avg. 1.20) | 10.0% to 15.0% (avg. 12.5%) |
| Liquid Alum | 1.32 to 1.34 (avg. 1.33) | 48.0% to 50.0% (dry equiv.) |
| Ferric Chloride | 1.38 to 1.45 (avg. 1.42) | 37.0% to 42.0% (FeCl3) |
| Sodium Hydroxide (50%) | 1.52 to 1.54 (avg. 1.53) | 50.0% (NaOH) |
| Sulfuric Acid (93%) | 1.83 to 1.84 (avg. 1.84) | 93.2% (H2SO4) |
+-----------------------------------------------------------------------------------------+
Determining Liquid Feed Rates (Gallons per Day & mL/min)
Once the pure chemical demand is established, the daily volumetric feed rate of liquid chemical is calculated:
Because metering pumps are calibrated in milliliters per minute (mL/min), the daily gallon feed rate must be converted using time and volumetric factors:
Dry Chemical Feeder Calibration & Catch Sampling
Dry chemical feeders (volumetric screw feeders, belt gravimetric feeders) require routine physical calibration. An operator places a catch container beneath the feed chute, collects chemical for a measured time duration (e.g., 5 or 10 minutes), and weighs the catch on a digital balance.
If the mass is measured in grams on a laboratory balance, convert grams to pounds by dividing by $453.6\text{ grams/lb}$:
Step-by-Step Worked Exam Calculations
Worked Example 1: Chlorine Gas Feed Rate
Problem: A water treatment plant treating a constant flow of $4.50\text{ MGD}$ maintains a primary chlorine disinfectant dosage of $2.80\text{ mg/L}$. Determine the required chlorine gas ($100%\ Cl_2$) feed rate setting in pounds per day.
Step 1: Apply the standard pounds formula.
Worked Example 2: Liquid Sodium Hypochlorite Dosing & Pump Calibration
Problem: A wastewater reclamation facility operates at a design effluent flow of $2.00\text{ MGD}$ and requires a chlorine disinfection dosage of $6.00\text{ mg/L}$. The plant feeds commercial sodium hypochlorite solution containing $12.5%$ available chlorine by weight with a Specific Gravity of $1.20$. Calculate:
- The daily pure chlorine demand in lbs/day.
- The active chlorine concentration in lbs per gallon of solution.
- The required liquid hypochlorite feed rate in gallons per day (GPD).
- The chemical metering pump calibration rate in milliliters per minute (mL/min).
Step 1: Calculate pure chlorine demand in lbs/day.
Step 2: Calculate active chlorine pounds per gallon of solution.
Step 3: Calculate liquid feed rate in gallons per day (GPD).
Step 4: Convert GPD to mL/min for pump calibration.
Worked Example 3: Calcium Hypochlorite (65%) Well Disinfection
Problem: A deep drinking water well casing and gravel pack contain a total static volume of $8,500\text{ gallons}$. Following maintenance, the well must be shock-chlorinated to an initial concentration of $150\text{ mg/L}$ using granular calcium hypochlorite ($65%$ available chlorine). How many pounds of granular product must be dissolved and introduced into the well?
Step 1: Calculate the pure chlorine mass required.
Step 2: Correct for 65% chemical purity.
A water treatment facility treats an average daily flow of 6.20 MGD. The operator adjusts the dry alum feeder to deliver a coagulation dosage of 22.0 mg/L. How many pounds of dry alum will the facility consume in a 24-hour period?
A water system uses a 15% sodium hypochlorite solution (Specific Gravity = 1.21) for pre-oxidation. What is the active chlorine concentration contained in one gallon of this chemical solution?
An operator calibrates a dry polymer feeder using a catch pan. Over a timed 5.0-minute catch interval, the operator collects exactly 315 grams of dry polymer. What is the calibrated feed rate in pounds per day?