Momentum Transfer and Transport Phenomena Lecture Notes

Comprehensive practice flashcards covering transport phenomena, fluid dynamics, and dimension analysis based on lecture transcript for Momentum Transfer.

Unit Operations

Processes that do not have any chemical reaction.

Unit Process

Operations that involve chemical reactions.

Momentum Transport Mechanism

Involves collisions where molecular momentum is passed from high velocity to low velocity molecules of the product of the mass and velocity of the particle.

Momentum Formula

$$P = \rho V$$

Molecular Transport

A mechanism that can be thought of as orderly but slow; for example, water becoming cold eventually without being stirred.

Turbulent Transport

A mechanism that can be thought of as chaotic but fast; for example, stirring water to speed up the cooling process.

Transport Phenomena

Irreversible processes that involve the exchange or transfer of momentum, heat, and mass.

Scalar (0th order tensor)

Mathematical objects that possess physical magnitude only, such as temperature, pressure, and concentration.

Vector (1st order tensor)

Mathematical objects that possess magnitude and direction, such as velocity, momentum, and force.

Dyad (2nd order tensor)

Mathematical objects that require magnitude and two directions or indices to specify their value, such as momentum flux and shear stress.

Continuity Equations

Physical laws describing how a quantity, such as mass or energy, is conserved (e.g., mass can neither be created nor destroyed).

Constitutive Equations

Also known as phenomenological rate or transport laws, these describe how a quantity responds to external stimuli via transport.

General Transport Equation

$$\text{Rate} = \frac{\text{Driving Force}}{\text{Resistance}}$$

General Molecular Transport Law

$\text{flux} = -\text{diffusivity} \times \frac{d(\text{concentration})}{dz}$ or $\frac{\text{property}}{\text{time} \times \text{area}} = -\text{diffusivity} \times \frac{d(\text{concentration})}{dz}$

Newton's Law of Viscosity

$$\tau_{zx} = -\nu \frac{d(u_x \rho)}{dz}$$

Momentum Diffusivity

Also known as kinematic viscosity ($\nu$), it is the ratio of viscosity to density, with units in $\text{m}^2/\text{s}$.

Fourier's Law of Heat Conduction

$$\frac{q_z}{A} = -k \frac{dT}{dz}$$

Fick's Law of Diffusion

$$J_{Az} = -D_{AB} \frac{dC_A}{dz}$$

Dynamic Viscosity (Centipoise)

$1000 \text{ cP} = 1 \text{ kg} \text{ m}^{-1} \text{ s}^{-1}$ and $1 \text{ Pa} \text{ s} = 1000 \text{ cP}$.

Reynolds Number ($N_{Re}$)

The ratio of inertial forces to the viscous forces within the fluid: $N_{Re} = \frac{L u \rho}{\rho}$. Below $2100$ is laminar, above $4000$ is turbulent.

Concept of Continuum

An assumption that fluid is continuously distributed throughout a region with no gaps between molecules.

Specific Weight ($\text{gamma}$)

Defined as the weight per unit volume: $\text{gamma} = \rho \frac{g}{g_c}$.

Pascal's Law

States that a change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points and acts at right angles to the walls.

Lapse Rate

The rate at which the temperature decreases with altitude ($L = -\frac{dT}{dz}$); for the troposphere, it is $6.4964 \text{ } ^{\text{o}}\text{C/km}$.

Standard Atmospheric Pressure

$101,325 \text{ Pa}$, $14.696 \text{ psia}$, or $760 \text{ mm Hg}$ ($0 \text{ } ^{\text{o}}\text{C}$).

Choked Flow

A limiting condition in adiabatic frictional flow where the mass flow rate cannot increase with further decrease in downstream pressure for a fixed upstream state.

Pitot-static Probe

A flowmeter that measure stagnant and static pressures to determine local velocity.

Venturi Meter Coefficient ($C_v$)

Typically equal to $0.98$ for pipelines between $2$ and $8 \text{ inches}$, used in variable-head flow measurement.

Mach Number ($N_{Ma}$)

The ratio of the speed of the fluid ($u$) to the speed of sound ($a$) in the fluid: $N_{Ma} = \frac{u}{a}$.

Planck Constant

$h = 6.626 070 15 \times 10^{-34} \text{ Js}$.

Avogadro Constant

$N_A = 6.022 140 76 \times 10^{23} \text{ mol}^{-1}$.