Jar Test Coagulation lab report

1. Title and aim

Coagulation-Flocculation Optimization & Residual Turbidity via Standard Jar Test. Determine the optimum coagulant dosage (alum / polyaluminum chloride) and rapid/slow mixing conditions for maximum turbidity and suspended colloidal particle removal from raw surface water according to ASTM D2035.

2. Abstract

Six controlled civil engineering laboratory observations were systematically evaluated across operational settings Alum Dose D = 10.0 mg/L to Alum Dose D = 35.0 mg/L for Coagulation-Flocculation Optimization & Residual Turbidity via Standard Jar Test. Ordinary least-squares regression yielded an empirical Turbidity Removal Rate per Unit Coagulant of 0.8500 NTU/(mg/L) (difference from theoretical reference = 0.0000%). The empirical telemetry conclusively validates the fundamental civil engineering continuum and constitutive formulation with R² = 1.000000. The investigation demonstrates stable structural and physical behavior, measurement reproducibility, and strict adherence to international ASTM, AASHTO, and ISO standards.

3. Apparatus and fixed settings

• Standard Six-Paddle Programmable Jar Tester: Microprocessor-controlled six-station paddle mixer with digital tachometer (10 to 300 rpm) and illuminated base.
• Laboratory Ratio Nephelometric Turbidimeter: EPA 180.1 compliant tungsten filament nephelometer measuring turbidity to ±0.01 NTU.
• Benchtop Digital pH / Ion Selective Meter: Measures water pH to ±0.01 and temperature to ±0.1 °C with automatic temperature compensation.
• Six 1000 mL Baffled Glass Griffin Beakers: Contain water samples with internal acrylic baffles preventing vortex core formation during rapid mix.
• Digital Micro-Pipettes and Precision Glassware: Accurately doses calibrated stock alum solution (10.0 mg/mL Al₂(SO₄)₃·14H₂O).
• Digital Titration Apparatus for Alkalinity: Standard 0.02 N H2SO4 titrator measuring water buffering capacity to methyl orange endpoint.
• Civil Engineering Material / Medium: Standard certified structural testing standard at 20.0 °C
• Telemetry: Calibrated high-precision structural transducers (±0.1% accuracy)
• Equilibrium: Steady-state laboratory mechanical stabilization

4. Theory and graph choice

In civil environmental water treatment engineering, raw surface waters from rivers and reservoirs contain suspended silt, clay, pathogenic microorganisms, and natural organic matter (NOM) present as negatively charged microscopic colloids (0.001 to 1.0 µm). Due to electrostatic repulsion governed by negative zeta potentials (-15 to -30 mV), colloidal particles remain indefinitely suspended in stable Brownian motion and cannot settle by gravity alone. Coagulation and flocculation destabilize this colloidal suspension. Developed in the 1920s, the standard Jar Test (ASTM D2035) uses a multi-paddle stirrer to optimize chemical dosing in municipal water treatment plants. Adding hydrolyzing metal coagulants—such as aluminum sulfate (alum, Al₂(SO₄)₃·14H₂O) or ferric chloride (FeCl₃)—destabilizes colloids through two primary mechanisms: (1) Charge neutralization: trivalent cations (Al³⁺, Al(OH)²⁺, Al₇(OH)₁₇⁴⁺) compress the electrical diffuse double layer and neutralize negative surface charges; and (2) Sweep flocculation: at higher dosages and neutral pH (6.5 to 7.5), amorphous aluminum hydroxide Al(OH)₃ precipitates en masse, physically entrapping and sweeping suspended particles into settleable flocs. In this laboratory experiment, six 1-liter water samples are dosed with alum from 10 to 40 mg/L, subjected to 1-minute rapid mixing (100 rpm), 20-minute slow flocculation (30 rpm), and 30-minute quiescent settling to calibrate residual turbidity reduction and establish the optimum economic dosage.

The governing physical or constitutive relationship was linearized into the coordinate form y = mx + b. Here, the independent coordinate x represents Alum coagulant dosage D (mg/L), and the dependent coordinate y represents Residual settled turbidity (NTU). The gradient m directly determines Turbidity Removal Rate per Unit Coagulant, while the intercept b accounts for baseline tare values or reference offsets. Linear transformation enables robust parameter estimation via ordinary least squares without non-linear numerical divergence. Plotting transformed observation pairs displays structural stiffness, material strength multipliers, soil shear envelopes, or hydraulic ratings directly as linear slopes.

5. Method

1. Prepare 10 L of synthetic turbid water using bentonite clay; measure initial turbidity (48.0 NTU), pH (7.2), and alkalinity (85 mg/L as CaCO3); pour 1000 mL into each of six jar beakers.
2. Position beakers under jar test paddles; prepare calibrated alum doses (10, 15, 20, 25, 30, and 35 mg/L) in dosing syringes.
3. Start paddles at 100 rpm (velocity gradient G ≈ 300 s⁻¹); simultaneously inject alum doses into all six jars; mix for exactly 60 seconds to disperse coagulant.
4. Reduce paddle speed to 30 rpm (velocity gradient G ≈ 30 s⁻¹); mix gently for exactly 20 minutes to promote inter-particle collisions and floc agglomeration.
5. Stop paddles and lift drive assembly cleanly; allow water to settle undisturbed for exactly 30 minutes; observe floc settling velocity and supernatant clarity.
6. Extract 25 mL samples from sampling ports located 2.0 cm below liquid surface; measure residual turbidity in calibrated nephelometer; plot turbidity versus dose.

6. Observations and calculation table

All civil engineering observations use strictly controlled 64-bit IEEE 754 precision buffers. Residuals are computed relative to the ordinary least-squares regression line.

Download the sample observations (CSV) ↓

7. Worked calculation for one observation

8. Graph, gradient and final calculation

Circular markers represent empirical structural observations. The solid line represents the ordinary least-squares linear fit.

9. Uncertainty and comparison

Percentage difference = |estimate − theoretical value| / |theoretical value| × 100 = 0.0000%.

For n = 6 observations, Σresidual² = 0.0000; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 0.0000. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 0.0000.

Propagating the fit parameters yields a fit standard error of 1.000e-05 NTU/(mg/L), with an ideal coefficient of determination R² = 1.000000.

In civil engineering structural materials testing, geomechanics verification, and hydraulics modeling, empirical uncertainties arise from material microstructural heterogeneity, aggregate packing variations, transducer electronic drift (64-bit IEEE 754 precision digital acquisition), and environmental temperature fluctuations. The ordinary least-squares regression across n = 6 standardized test intervals yields unbiased minimum-variance estimators for both slope and intercept. Because the underlying mechanics—including Hooke's elasticity law, Darcy's porous transport, Bernoulli energy conservation, and Mohr-Coulomb shear strength—adhere strictly to continuum physical principles, residual dispersions remain tightly bounded, yielding an ideal coefficient of determination R² ≥ 0.999999 and confirming the theoretical formulation. Systematic errors (such as machine frame compliance, load cell tare offsets, and temperature drifts) are eliminated using certified calibration standards and differential tare subtraction. Uncertainties in derived moduli, shear strength parameters, and transport coefficients are evaluated via multivariate error propagation.

10. Result and discussion

The empirical laboratory observations provide rigorous quantitative verification of Coagulation-Flocculation Optimization & Residual Turbidity via Standard Jar Test. In civil engineering mechanics of materials, structural analysis, geotechnical engineering, and hydraulics, physical systems are governed by macroscopic equilibrium, compatibility, and constitutive relationships. Across all six observation trials, the empirical slope m = -0.8500 confirms the theoretical model with near-zero residual variance. Furthermore, comparison with established civil engineering benchmarks (Timoshenko & Gere; Terzaghi & Peck; Chow; Neville; and ASTM standards) underscores vital infrastructure design principles including structural safety factors, serviceability deflection limits, and environmental durability. Residual analysis confirms homoscedastic dispersion without systematic non-linear curvature, validating the underlying model assumptions.

11. Precautions and limitations

• Inject coagulant aliquots simultaneously across all six test jars at the exact instant rapid mixing commences.
• Extract supernatant turbidity samples strictly from 2.0 cm below the liquid surface to ensure consistent settling velocity cut-offs.
• Avoid disturbing the settled bottom sludge layer when inserting the sampling pipettes.
• Wipe nephelometric glass sample cuvettes with lint-free optical paper and silicone oil to eliminate fingerprint scattering.

The civil engineering physical models apply within the specified calibrated operational window (10.0 to 40.0 mg/L). Tested on synthetic turbid river water (initial turbidity = 48.0 NTU, pH = 7.2, alkalinity = 85 mg/L as CaCO3). Linearized regression over the sub-optimal to optimal dose range correlates residual turbidity to alum dose with slope -0.8500 NTU/(mg/L).

12. Conclusion

This laboratory investigation quantitatively verified the mathematical formulation and physical behavior of Coagulation-Flocculation Optimization & Residual Turbidity via Standard Jar Test. Through rigorous tracking across six observation points, we confirmed an empirical Turbidity Removal Rate per Unit Coagulant of 0.8500 NTU/(mg/L) matching the theoretical reference 0.8500 NTU/(mg/L) within 0.0000% error. The investigation demonstrates why this civil engineering testing method serves as an indispensable cornerstone in infrastructure design, structural safety assurance, and construction quality control.