Particle Characteristics, Water Chemistry and Thermal Pollution: 18-Env-A1 Principles of Environmental Engineering, May 2014, Q3

Question 3: Particle Characteristics, Water Chemistry and Thermal Pollution (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(i) Sedimentation and Filtration for Particle Removal

Sedimentation and filtration are complementary, sequential unit processes rather than interchangeable ones. Sedimentation (following coagulation/flocculation, which destabilizes colloidal particles and grows them into settleable flocs) removes the coarse fraction of particles by gravity settling in a quiescent basin sized from the particles' settling velocity and the basin's surface overflow rate; it is efficient and low-cost for the bulk mass of solids but cannot remove the residual fine floc and colloidal material that settle too slowly to clarify within a practical basin depth and detention time. Filtration (typically rapid sand or dual-media, deep-bed filtration) then polishes that settled water by passing it through a granular media bed, where the remaining fine particles are removed by a combination of straining, interception, sedimentation within the pore spaces, and adsorption onto the media grains — mechanisms that are only economical once sedimentation has already stripped out the bulk solids load, because an unsettled high-turbidity feed would clog and rapidly exhaust the filter bed. Used together, the pair routinely reduces raw-water turbidity from tens of NTU to well under 1 NTU, which is what makes the subsequent disinfection step (see Q1(iii)) effective, since particles can shield pathogens from disinfectant contact.

Figure 3.1 — Conventional particle-removal train: coagulated/flocculated raw water passes through a sedimentation basin (which removes the bulk floc and produces settled sludge for disposal) before a rapid sand filter polishes the settled water to low turbidity, backwashing periodically to a sludge-handling system.

(ii) Hardness of Lake Superior Water Near the Salt Mine

Given. Divalent-cation concentrations from the water analysis, with atomic weights Ca = 40, H = 1, C = 12, O = 16 as stated (magnesium's standard atomic weight, 24.3, is assumed general knowledge since it is not on the supplied list):

Given data
Ion	Concentration	Atomic weight	Valence
$Ca^{2+}$	90 mg/L	40 (given)	2
$Mg^{2+}$	100 mg/L	24.3 (standard)	2
$Cu^{2+}$	50 mg/L	63.5 (standard)	2

Find. The total hardness of the water expressed as mg/L CaCO₃, and its qualitative classification (soft, moderately hard or hard).

Check: hardness is defined as the sum of polyvalent alkaline-earth metal cations in water, of which $Ca^{2+}$ and $Mg^{2+}$ are overwhelmingly dominant in natural waters; standard water-chemistry practice (and the fact that no atomic weight for copper was supplied on the exam's own aid-sheet list) treats $Cu^{2+}$ here as a trace heavy-metal constituent reported alongside the hardness-forming ions, not as a contributor to the hardness figure itself. The calculation below therefore uses $Ca^{2+}$ and $Mg^{2+}$ only; for reference, including $Cu^{2+}$ as if it were hardness-forming would add a further 78.7 mg/L as CaCO₃, which does not change the classification.

Approach. Convert each hardness-forming ion's mass concentration to an equivalent mass concentration as $\text{CaCO}_3$ using the ratio of equivalent weights, then sum and classify against the standard hardness scale.

Equivalent weight of $\text{CaCO}_3$. Molecular weight $= 40 + 12 + 3(16) = 100\ \text{g/mol}$; with valence 2 (each $\text{CO}_3^{2-}$ neutralizes one divalent cation), $$EW_{CaCO_3} = \frac{100}{2} = 50\ \text{g/eq}.$$
Convert $Ca^{2+}$ to CaCO₃ equivalent. $EW_{Ca} = 40/2 = 20\ \text{g/eq}$, so $$H_{Ca} = 90 \times \frac{50}{20} = \boxed{225.0\ \text{mg/L as CaCO}_3}.$$
Convert $Mg^{2+}$ to CaCO₃ equivalent. $EW_{Mg} = 24.3/2 = 12.15\ \text{g/eq}$, so $$H_{Mg} = 100 \times \frac{50}{12.15} = \boxed{411.5\ \text{mg/L as CaCO}_3}.$$
Total hardness and classification. Summing the hardness-forming ions, $$H_{total} = H_{Ca} + H_{Mg} = 225.0 + 411.5 = \boxed{636.5\ \text{mg/L as CaCO}_3}.$$ Against the standard scale (<75 soft; 75–150 moderately hard; 150–300 hard; >300 very hard), 636.5 mg/L is far above the 300 mg/L threshold — the water is classified as hard (at the extreme, "very hard," end of that category), consistent with dissolution of evaporite salts (gypsum/dolomite) near the salt mine.

Quantity	Value
Hardness from $Ca^{2+}$	225.0 mg/L as CaCO₃
Hardness from $Mg^{2+}$	411.5 mg/L as CaCO₃
Total hardness	636.5 mg/L as CaCO₃
Classification	Hard (very hard)

(iii) Downstream Mixed Temperature and Cold-Water Fishery Protection

Given. Flow rates and temperatures of the two streams mixing in the river:

Given data
Quantity	Symbol	Value
Heated discharge flow	$Q_c$	100 m³/s
Heated discharge temperature	$T_c$	35°C
Upstream river temperature	$T_s$	15°C
Combined downstream flow	$Q$	200 m³/s

Figure 3.2 — Mixing of the upstream river flow ($Q_s$, inferred by continuity as $Q-Q_c$) with the heated discharge ($Q_c$) to give the combined downstream flow $Q$ at unknown mixed temperature $T$.

Find. The combined downstream river temperature $T$.

Approach. The upstream river flow $Q_s$ is not stated directly but is fixed by continuity ($Q = Q_s + Q_c$); a steady-flow thermal energy balance (constant density and specific heat) on the mixing point then gives the combined temperature as a flow-weighted average.

Find the upstream river flow by continuity. $$Q_s = Q - Q_c = 200 - 100 = 100\ \text{m}^3/\text{s}.$$
Write the thermal energy balance at the mixing point. With constant $\rho$ and $c_p$, the energy balance reduces to a flow-weighted temperature average: $$Q\,T = Q_s T_s + Q_c T_c \quad\Rightarrow\quad T = \frac{Q_s T_s + Q_c T_c}{Q}.$$
Substitute and solve. $$T = \frac{(100)(15) + (100)(35)}{200} = \frac{1500 + 3500}{200} = \boxed{25.0\,{}^{\circ}\text{C}}.$$

Quantity	Value
Upstream river flow (by continuity), $Q_s$	100 m³/s
Combined downstream temperature, $T$	25.0 °C

A downstream temperature of 25°C is well above the roughly 10–19°C range most cold-water salmonid fisheries need, so the discharge is a genuine thermal-pollution concern. Two engineering solutions to reduce it: (1) install a cooling tower or cooling pond on the discharge so heat is rejected to the atmosphere before the water re-enters the river, cutting $T_c$ (and hence the mixed $T$) directly; and (2) use a diffuser outfall that discharges the heated flow as many small, high-velocity jets across the river's width/depth rather than one concentrated point source, which does not reduce the total heat load but rapidly entrains additional river water into the near-field mixing zone, lowering the peak temperature any single fish encounters and shortening the reach of water above the fishery's thermal tolerance.

Concept & Theory

Topic. Physical/chemical unit processes (sedimentation, filtration), water chemistry (hardness), and thermal energy balances in surface-water quality engineering.

Key relations. Settling-velocity/overflow-rate design for sedimentation; hardness as CaCO₃, $H = \sum C_i \cdot (50/EW_i)$; steady-flow thermal mixing, $T = (Q_sT_s+Q_cT_c)/Q$.

Why this works. Each sub-part is a mass or energy balance applied to a different quantity carried by water — suspended solids, dissolved divalent cations, and thermal energy — and in every case an engineered process (a basin, a chemical equivalence, a mixing zone) is sized or evaluated from that balance rather than from rules of thumb.

Common pitfall. Skipping straight to filtration sizing without recognizing sedimentation's role in protecting the filter run length; including every reported cation (e.g., $Cu^{2+}$) in a hardness sum without checking whether it is actually a hardness-forming species; forgetting that a downstream flow given in a mixing problem usually fixes the "missing" upstream flow by continuity.

Source. MWH’s Water Treatment: Principles and Design, sedimentation and filtration chapters; Davis & Cornwell, Introduction to Environmental Engineering, ch. 5 (water chemistry, hardness) and ch. 9 (thermal pollution).

Question 3 of 7: Particle Characteristics, Water Chemistry and Thermal Pollution

Question 3: Particle Characteristics, Water Chemistry and Thermal Pollution (20 marks)

(i) Sedimentation and Filtration for Particle Removal

(ii) Hardness of Lake Superior Water Near the Salt Mine

(iii) Downstream Mixed Temperature and Cold-Water Fishery Protection