16.2 Dosage, Chemical Feed & Detention Time

16.2 Dosage, Chemical Feed & Detention Time

Quick Answer: Chemical feed in lb/day uses MGD × mg/L × 8.34. Liquid feed from a percent solution converts pure chemical mass to gpd of product. Detention time is volume ÷ flow with consistent units. Pump calibration by drawdown measures actual feed or flow from a drop in a calibration cylinder or tank over a timed interval.

Process control is quantitative: chlorine residual targets, coagulant doses, polymer feeds, and basin contact times all reduce to a few repeatable setups. Master them cold for Florida Class C and distribution exams.

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1. The Pounds Formula (Dosage / Feed Rate)

$$\text{Feed rate (lb/day)} = Q\ (\text{MGD}) \times \text{Dose (mg/L)} \times 8.34$$

Demand vs dose vs residual (chlorine story):

$$\text{Dose} \approx \text{Demand} + \text{Residual}$$

If demand is 1.2 mg/L and residual target is 1.0 mg/L, applied dose ≈ 2.2 mg/L (idealized; real systems include losses and mixing).

Worked Example 1 — Chlorine Gas Feed (lb/day)

Plant flow 2.5 MGD. Operator applies 2.0 mg/L free chlorine dose.

$$\text{lb/day} = 2.5 \times 2.0 \times 8.34 = 41.7\ \text{lb/day}$$

Interpretation: About 42 lb/day chlorine gas (or equivalent available chlorine) must be fed at that flow and dose. If flow doubles and dose stays the same, feed doubles.

Worked Example 2 — Find Required Dose from Feed Rate

A chlorinator is set to 25 lb/day. Flow is 1.2 MGD. What dose (mg/L) is being applied?

Rearrange:

$$\text{mg/L} = \frac{\text{lb/day}}{Q \times 8.34} = \frac{25}{1.2 \times 8.34} = \frac{25}{10.008} \approx 2.5\ \text{mg/L}$$

Worked Example 3 — Convert gpm Then Dose

Flow meter reads 800 gpm. Desired alum dose is 15 mg/L. Find lb/day.

Step 1 — MGD

$$800 \times 0.00144 = 1.152\ \text{MGD}$$

Step 2 — Pounds

$$1.152 \times 15 \times 8.34 = 1.152 \times 125.1 \approx 144.1\ \text{lb/day}$$

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2. Liquid Chemical Feed from Percent Strength

When the chemical is supplied as a solution or slurry of known percent by weight, first find pure chemical lb/day, then convert to solution lb/day and gpd.

$$\text{lb/day pure} = Q \times \text{mg/L} \times 8.34$$ $$\text{lb/day solution} = \frac{\text{lb/day pure}}{\text{decimal percent}}$$ $$\text{gpd solution} \approx \frac{\text{lb/day solution}}{8.34}$$

(Assumes solution density ≈ water; for dense chemicals some exams give specific gravity—then multiply 8.34 by S.G.)

With specific gravity:

$$\text{gpd} = \frac{\text{lb/day solution}}{8.34 \times \text{S.G.}}$$

Worked Example 4 — Hypochlorite Feed

Need 40 lb/day available chlorine. Product is 12% available chlorine, S.G. ≈ 1.0 for estimate.

$$\text{lb/day solution} = 40 / 0.12 = 333.3\ \text{lb/day}$$ $$\text{gpd} = 333.3 / 8.34 \approx 40.0\ \text{gpd}$$

Cross-check: At 12%, each gallon (~8.34 lb) carries $0.12 \times 8.34 ≈ 1.0$ lb available Cl₂, so 40 lb/day needs ~40 gpd—clean mental check.

Worked Example 5 — Polymer or Coagulant Percent Solution

Feed 12 lb/day active polymer from a 0.5% solution (S.G. = 1.0).

$$\text{lb/day solution} = 12 / 0.005 = 2{,}400\ \text{lb/day}$$ $$\text{gpd} = 2{,}400 / 8.34 \approx 288\ \text{gpd}$$

Weak solutions require large volumetric feeds—a common exam surprise.

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3. Detention Time (Hydraulic Retention)

$$t = \frac{V}{Q}$$

Minutes is the most common operator unit for basins and contact tanks:

$$t_{\text{min}} = \frac{V_{\text{gal}}}{Q_{\text{gpm}}}$$

Or:

$$t_{\text{min}} = \frac{V_{\text{gal}} \times 1{,}440}{Q_{\text{gpd}}}\quad\text{or}\quad t_{\text{hr}} = \frac{V_{\text{gal}}}{Q_{\text{gph}}}$$

Worked Example 6 — Tank Detention Time

Tank volume 50,000 gal. Flow 250 gpm.

$$t = 50{,}000 / 250 = 200\ \text{minutes} \approx 3.33\ \text{hours}$$

Worked Example 7 — Volume Needed for a Target DT

Want 30 minutes detention at 1,200 gpm.

$$V = t \times Q = 30 \times 1{,}200 = 36{,}000\ \text{gal}$$

Worked Example 8 — Chlorine Contact Using MG and MGD

Clearwell 0.25 MG, flow 2.0 MGD.

$$t_{\text{days}} = 0.25 / 2.0 = 0.125\ \text{day}$$ $$t_{\text{minutes}} = 0.125 \times 1{,}440 = 180\ \text{minutes}$$

CT link (concept): If residual C = 1.0 mg/L and theoretical T = 180 min, raw CT = 180 mg·min/L before baffling factors (see disinfection chapter for effective T).

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4. Pump Calibration — Drawdown Math

Chemical feed pumps and plant flow meters are verified by timed volume change in a calibration column or tank.

$$Q = \frac{\text{Volume pumped}}{\text{Time}}$$

Cylinder method (mL and minutes → mL/min or gpd):

If level drops $\Delta h$ in a cylinder of known area, volume = area × drop.

Worked Example 9 — Calibration Column

A calibration cylinder has cross-section such that 100 mL corresponds to a marked interval. Pump draws 250 mL in 2.0 minutes.

$$\text{Feed} = 250\ \text{mL} / 2.0\ \text{min} = 125\ \text{mL/min}$$

Convert to gpd if needed: $125\ \text{mL/min} \times 1{,}440\ \text{min/day} = 180{,}000\ \text{mL/day}$. Since 3,785 mL ≈ 1 gal, gpd ≈ $180{,}000 / 3{,}785 ≈ 47.6$ gpd.

Worked Example 10 — Wet Well or Tank Drop → gpm

A cylindrical wet well, D = 6 ft, water level drops 1.5 ft in 4 minutes with inflow isolated (pumping only).

Volume dropped (ft³):

$$V = 0.785 \times 6^2 \times 1.5 = 0.785 \times 36 \times 1.5 = 42.39\ \text{ft}^3$$

Gallons:

$$V = 42.39 \times 7.48 \approx 317\ \text{gal}$$

gpm:

$$Q = 317\ \text{gal} / 4\ \text{min} \approx 79\ \text{gpm}$$

This is the same skill used for pump capacity checks and some inflow estimates.

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5. Putting Dosage and Detention Together

Worked Example 11 — Mini Plant Scenario

Flow 1.5 MGD. Chlorine dose 1.8 mg/L. Contact basin 90,000 gal.

Feed:

$$1.5 \times 1.8 \times 8.34 = 22.5\ \text{lb/day approximately?}$$

Exactly: $1.5 \times 1.8 = 2.7$; $2.7 \times 8.34 = 22.518 ≈ 22.5$ lb/day.

Detention (minutes): First gpm = $1.5 / 0.00144 = 1{,}041.7$ gpm.

$$t = 90{,}000 / 1{,}041.7 \approx 86.4\ \text{minutes}$$

Or using days: (V = 0.09) MG; (t = 0.09/1.5 = 0.06) day × 1440 = 86.4 minutes.

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6. Exam Habits for Feed & DT Items

1. Underline the flow unit (gpm vs MGD) before writing the pounds formula.
2. Percent → decimal (12% → 0.12), never leave “12” in the denominator.
3. For DT, convert everything to gal and gpm or MG and MGD—do not mix.
4. Drawdown problems need geometry first, then ÷ time.
5. If choices are close, recompute with full precision and check S.G. note in the stem.

Florida exams reward operators who treat chemical feed as a mass balance, not a “set the dial and hope” skill. Calibration proves the pump delivers the calculated gpd.