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Essential CIH Equations & Constants

Jul 19, 2025

Overview

This lecture reviews essential equations, constants, and conversions relevant to the CIH (Certified Industrial Hygienist) examination, covering ventilation, noise, radiation, general sciences, and heat stress.

Ventilation Equations

  • Continuity: Q₁A₁ = Q₂A₂, where Q = flow rate and A = area.
  • Conservation: Q_total = Q₁ + Q₂, and 1/k_total = 1/k₁ + 1/k₂.
  • Pressure-velocity: V = 4005√ΔP (US), V = √(2ΔP/ρ) (SI).
  • Effective velocity: V = Q/A.
  • Losses: H = Σ(velocity head × loss coefficient).
  • Changes in conditions: Q₁P₁/T₁ = Q₂P₂/T₂.
  • Mixing: C = (Q₁C₁ + Q₂C₂)/(Q₁ + Q₂).
  • Fan laws: Q₂ = Q₁(N₂/N₁), P₂ = P₁(N₂/N₁)², HP₂ = HP₁(N₂/N₁)³.

Noise Equations

  • Sound level: dB = 20 log₁₀(P/P₀), where P = sound pressure.
  • Intensity: dB = 10 log₁₀(I/I₀), I = intensity.
  • Adding levels: dB_total = 10 log₁₀(Σ10^(dB_i/10)).
  • Dose calculation: % = 100(D₁/L₁ + D₂/L₂ + ...).
  • Exchange rate: L = 10 log₁₀(%/100) + 85 or L = 16.61 log₁₀(%/100) + 90.

General Sciences & Statistics

  • Gas laws: PV = nRT.
  • Standard conversions: 1 atm = 760 mmHg, 1 ft³ = 28.32 L.
  • Probability and statistics: Variance σ² = Σ(x-μ)²/N, Standard deviation σ = √variance.
  • Confidence intervals: 95% CI uses z = 1.96, 90% uses z = 1.645.
  • Weighted mean: μ = Σ(wₙxₙ)/Σwₙ.

Heat Stress Equations

  • Wet Bulb Globe Temperature (WBGT): WBGT = 0.7Tnwb + 0.2Tg + 0.1Tdb (indoors); WBGT = 0.7Tnwb + 0.3Tg (outdoors).
  • Metabolic rate: Heat = (Metabolic rate - External work).

Radiation Equations

  • Inverse square law: I₂ = I₁(d₁/d₂)².
  • Radioactive decay: N = N₀(0.5)^(t/T½).
  • Decay constant: λ = 0.693/T½.
  • Half-life: T½ = 0.693/λ.
  • O.D. (Optical Density): O.D. = log₁₀(I₀/I).

Constants & Conversions

  • Temp: F = 9/5(C) + 32, K = C + 273.15.
  • Vol: 1 ft³ = 28.32 L, 1 gal = 3.785 L.
  • Mass: 1 lb = 453.6 g, 1 g = 15.43 grains.
  • Pressure: 1 atm = 14.7 psi = 760 mmHg.
  • Energy: 1 BTU = 1054.8 J, 1 cal = 4.184 J.
  • Speed of sound (20°C): 344 m/s.
  • Avogadro's number: 6.024×10²³.
  • Gas constant, R: 8.314 J/mol·K.

Key Terms & Definitions

  • acfm — actual cubic feet per minute (airflow at actual conditions).
  • scfm — standard cubic feet per minute (airflow at standard conditions).
  • WBGT — Wet Bulb Globe Temperature, a heat stress index.
  • dB (decibel) — a logarithmic unit to measure sound intensity.
  • T½ (half-life) — time for a radioactive substance to halve its activity.

Action Items / Next Steps

  • Review actual equation sheet and familiarize yourself with variable meanings.
  • Reference Table 6-2 and Figure 9-a in the ACGIH Industrial Ventilation Manual as allowed during exam.
  • Practice applying these formulas to sample problems.