CIE 340 Environmental Engineering: Conservation Laws, Control Volumes, Mass, Energy, and Number Balances

Vocabulary flashcards covering core concepts of conservation laws, reactor dynamics, energy balances, population number balances, and qualitative risk analysis.

Conservation Laws

Principles stating that primary properties—specifically mass, energy, linear and angular momentum, and charge—do not change over time in isolated systems.

Control Volume

An isolated spatial system bounded in space and time (usually indicated by a dashed line) to which conservation laws are applied.

General Conservation Statement

The fundamental rate equation stating that the rate of accumulation of a property inside a control volume equals the rate in minus the rate out plus the rate of utilization inside.

Continuous Stirred-Tank Reactor (CSTR)

A reactor model featuring continuous inflow and outflow with well-mixed internal conditions, resulting in an effluent concentration equal to the internal concentration ($C_{\text{out}} = C$) and steady-state concentration $C = \frac{C_{\text{in}}}{1 + k\theta}$.

Plug Flow Reactor (PFR)

A reactor model characterized by continuous fluid flow along a path with no axial mixing, yielding a steady-state effluent concentration of $C = C_{\text{in}}e^{-k\theta}$.

Batch Reactor

A well-mixed reactor system with no continuous inflow or outflow ($Q = 0$), where first-order substance disappearance follows the non-steady-state equation $C = C_0 e^{-kt}$.

Retention Time ($\theta$)

The average residence time of fluid in a system, calculated as volume divided by volumetric flow rate ($\theta = \frac{V}{Q}$).

Differential Form of the Energy Balance

An energy balance equation expressing rates where energy accumulation rate equals energy rate in minus energy rate out plus energy utilization rate, with terms in units of energy per time ($\text{J/s}$ or $\text{W}$).

Integral Form of the Energy Balance

An energy balance equation where total change in internal energy ($\Delta E$) equals energy in minus energy out plus sources minus sinks, with all terms expressed in units of energy ($\text{J}$).

Specific Heat

The thermal property defining a substance's temperature response to heat absorption, expressed through the internal energy equation $\Delta E = mc\Delta T$.

Exponential Growth

Population growth where net growth rate is directly proportional to population ($+rN$), resulting in $N = N_0 e^{+rt}$ when no transport occurs across the control volume.

Logistic Growth Rate

A resource-limited population growth model where the net growth rate decreases as population increases, given by $+\left(1 - \frac{N}{K}\right)rN$.

Carrying Capacity ($K$)

The maximum population size of a species that an ecosystem or environment can sustain indefinitely.

Maximum Sustainable Yield (MSY)

The maximum harvesting rate that maintains a constant resource population, occurring at $N = \frac{K}{2}$ with rate $\text{MSY} = \frac{rK}{4}$.

Population Momentum

The concept that a population continues to grow while policy changes and interventions aimed at slowing growth are being implemented.

Dose-Response Curve

An S-shaped graph plotting biological response (dimensionless risk) against chemical dose (in $\text{mg/kg-d}$), with environmental engineering focusing on low-dose and low-response regions.

Carcinogens

Cancer-causing agents assumed to have no safe threshold dose, whose potency is quantified by the slope of their dose-response curve.

Non-Carcinogens

Substances that do not cause cancer and possess a safe threshold dose, quantified using a reference dose ($\text{RfD}$).

Slope Factor

The slope of the dose-response curve for carcinogens (also called potency factor), representing cancer risk per unit dose with typical units of $(\text{mg/kg-d})^{-1}$.

Reference Dose ($\text{RfD}$)

The safe threshold intake level for non-carcinogens, defined as the no-observable-effects dose divided by a safety factor.

River Confluence Mixing Model

A steady-state mass balance mixing process where wastewater ($Q_W, C_W$) mixes with river flow ($Q_R, C_R$) to form a combined downstream flow $Q = Q_R + Q_W$ and concentration $C = \frac{Q_R C_R + Q_W C_W}{Q_R + Q_W}$.

CSTRs in Series Configuration

A treatment train of sequential continuous stirred-tank reactors where the steady-state effluent concentration of the first basin ($C_1 = \frac{C_{\text{in}}}{1 + k\theta_1}$) serves as the influent concentration to calculate the second basin effluent ($C_2 = \frac{C_1}{1 + k\theta_2}$).

Solar Collector Energy System

An energy balance control volume where solar energy flux transferred to water flowing at rate $Q$ causes a temperature increase calculated using $\text{energy rate in} = c \frac{dm}{dt} \Delta T$.

Power Plant Heat Dissipation Model

A steady-state energy balance for a power facility where total energy rate in equals electric power generated plus thermal waste energy carried away by cooling water flow ($c\rho Q\Delta T$).