Environmental and Water Resources Review

Overview

This lecture reviewed key concepts and problem types from the Environmental and Water Resources section of the FE exam, covering fluid mechanics, hydraulics/hydrology, and environmental engineering applications.

FE Exam Topic Breakdown

• Fluid mechanics, hydraulics/hydrology, and environmental engineering make up ~23% of the FE exam.
• Fluid mechanics focuses on properties, measurement, statics, energy, impulse/momentum, ideal gas law, and Bernoulli’s and continuity equations.
• Hydraulics and hydrology stress Manning’s and Hazen-Williams equations, pipe and open channel flow, and municipal water systems.
• Environmental engineering addresses water/wastewater treatment, water quality, regulations, and excludes air/solid waste in the latest exams.

Fluid Mechanics Key Concepts

• Ideal Gas Law: PV = nRT; use consistent units (P in Pascals, T in Kelvin, R = 8.314 J/mol·K).
• Hydrostatics: Resultant force on submerged surfaces acts at 1/3 the height from the base.
• Viscosity: Defined as shear stress divided by rate of shear deformation (Newton’s law of viscosity).
• Momentum Equation: Forces on deflection plates solved via control volumes and conservation of momentum.
• Bernoulli’s Equation: For steady, incompressible, frictionless flow; be cautious of unit conversions.

Hydraulics and Hydrology Problems

• Manning’s Equation (velocity): V = (K/n)R^(2/3)S^(1/2), where R = area/wetted perimeter, S = slope (convert % to ft/ft).
• Manning’s Equation (flow rate): Q = (K/n)A R^(2/3) S^(1/2); ensure diameter is in feet.
• Friction Slope: Use water surface elevation, not invert, for slope in sewer questions.
• Hazen-Williams Equation: Used for head loss in pipes; velocity = 1.38 C R^0.63 S^0.54, use diameter in feet.
• Head Loss Calculation: ΔH = (pipe length) × (friction slope); be careful with small-diameter, high-velocity pipes.

Environmental Engineering Applications

• Oxygen Demand Calculation: Balance reaction, convert concentrations to moles, use stoichiometry to determine O2 needed for biodegradation.
• BOD (Biochemical Oxygen Demand) Mixtures: Resulting BOD = weighted average including all flows, even clean inflows (infiltration).
• Wastewater Plant Efficiency: Removal in steps uses mass balances; conversion factor is 8.34 lb/(mg/L·MGD).
• Residence Time and Basin Volume: Volume = flow rate × residence time (convert between hours and days as needed).

Key Terms & Definitions

• Specific Weight (γ) — Weight per unit volume, γ = ρg.
• Hydraulic Radius (R) — Cross-sectional area divided by wetted perimeter.
• Viscosity (μ) — Ratio of shear stress to rate of deformation.
• Manning’s n — Empirical roughness coefficient for open channel flow.
• Hazen-Williams C — Pipe material-dependent roughness coefficient.

Action Items / Next Steps

• Practice additional FE review problems on hydrology and hydraulics.
• Review stoichiometry and mass balance for water and wastewater problems.
• Pay close attention to unit conversions in all calculations.