Fluid Mechanics and Heat Transfer: Dimensions and Units

Vocabulary flashcards detailing physical quantities, symbols, SI units, and MLT/MLTΘ dimensional representations in fluid mechanics and thermodynamics.

Force, Drag

Symbols: $F, D$; SI Units: $\text{N} = \text{kg}\cdot\text{m}/\text{s}^2$; Dimensions: $\text{MLT}^{-2}$

Pressure, Stress, Shear, Elastic Modulus

Symbols: $p, \tau, E$; SI Units: $\text{Pa} = \text{N}/\text{m}^2 = \text{kg}/(\text{m}\cdot\text{s}^2)$; Dimensions: $\text{ML}^{-1}\text{T}^{-2}$

Pressure Gradient ($dp/dx, G, \Delta p/L$)

Symbol: $dp/dx$; SI Units: $\text{Pa}/\text{m} = \text{N}/\text{m}^3$; Dimensions: $\text{ML}^{-2}\text{T}^{-2}$

Specific Weight ($\rho g$)

Symbol: $\rho g$; SI Units: $\text{N}/\text{m}^3$; Dimensions: $\text{ML}^{-2}\text{T}^{-2}$

Density

Symbol: $\rho$; SI Units: $\text{kg}/\text{m}^3$; Dimensions: $\text{ML}^{-3}$

Dynamic Viscosity

Symbol: $\mu$; SI Units: $\text{kg}/(\text{m}\cdot\text{s}) = \text{Pa}\cdot\text{s} = \text{N}\cdot\text{s}/\text{m}^2$; Dimensions: $\text{ML}^{-1}\text{T}^{-1}$

Kinematic Viscosity ($\mu/\rho$)

Symbol: $\nu$; SI Units: $\text{m}^2/\text{s}$; Dimensions: $\text{L}^2\text{T}^{-1}$

Velocity

Symbols: $V, U, u$; SI Units: $\text{m}/\text{s}$; Dimensions: $\text{LT}^{-1}$

Acceleration, Gravity

Symbols: $a, g$; SI Units: $\text{m}/\text{s}^2$; Dimensions: $\text{LT}^{-2}$

Volume Flow Rate

Symbol: $Q$; SI Units: $\text{m}^3/\text{s}$; Dimensions: $\text{L}^3\text{T}^{-1}$

Flow Rate Per Unit Width

Symbol: $q = Q/b$; SI Units: $\text{m}^2/\text{s}$; Dimensions: $\text{L}^2\text{T}^{-1}$

Mass Flow Rate

Symbol: $\dot{m}$; SI Units: $\text{kg}/\text{s}$; Dimensions: $\text{MT}^{-1}$

Stream Function

Symbol: $\psi$; SI Units: $\text{m}^2/\text{s}$; Dimensions: $\text{L}^2\text{T}^{-1}$

Velocity Potential

Symbol: $\varphi$; SI Units: $\text{m}^2/\text{s}$; Dimensions: $\text{L}^2\text{T}^{-1}$

Vorticity, Strain Rate, Frequency

Symbols: $\omega, du/dy, f$; SI Units: $1/\text{s}$; Dimensions: $\text{T}^{-1}$

Head ($h_f$, HGL, $\delta$, $\theta$, $\delta^*$, $\varepsilon$)

Symbols: $h, \delta\dots$; SI Units: $\text{m}$; Dimensions: $\text{L}$

Energy, Work, Torque

Symbols: $E, W, T$; SI Units: $\text{J} = \text{N}\cdot\text{m}$; Dimensions: $\text{ML}^2\text{T}^{-2}$

Power

Symbol: $P$; SI Units: $\text{W} = \text{J}/\text{s}$; Dimensions: $\text{ML}^2\text{T}^{-3}$

Surface Tension

Symbols: $\Upsilon, \sigma$; SI Units: $\text{N}/\text{m}$; Dimensions: $\text{MT}^{-2}$

Area Moment of Inertia (beams, P5.23)

Symbol: $I$; SI Units: $\text{m}^4$; Dimensions: $\text{L}^4$

Mass Moment of Inertia (rotation)

Symbols: $I, J$; SI Units: $\text{kg}\cdot\text{m}^2$; Dimensions: $\text{ML}^2$

Mass Per Unit Length (beams)

Symbol: $m'$; SI Units: $\text{kg}/\text{m}$; Dimensions: $\text{ML}^{-1}$

Stiffness (spring)

Symbol: $k$; SI Units: $\text{N}/\text{m}$; Dimensions: $\text{MT}^{-2}$

Damping Coefficient

Symbol: $c$; SI Units: $\text{N}\cdot\text{s}/\text{m} = \text{kg}/\text{s}$; Dimensions: $\text{MT}^{-1}$

Gas Constant (specific)

Symbol: $R$; SI Units: $\text{J}/(\text{kg}\cdot\text{K})$; Dimensions: $\text{L}^2\text{T}^{-2}\Theta^{-1}$

Universal Gas Constant

Symbol: $\bar{R}$; SI Units: $\text{J}/(\text{mol}\cdot\text{K})$; Dimensions: (per mole)

Specific Heat

Symbols: $c_p, c_v$; SI Units: $\text{J}/(\text{kg}\cdot\text{K})$; Dimensions: $\text{L}^2\text{T}^{-2}\Theta^{-1}$

Thermal Conductivity

Symbol: $k$; SI Units: $\text{W}/(\text{m}\cdot\text{K})$; Dimensions: $\text{MLT}^{-3}\Theta^{-1}$

Viscous Dissipation

Symbol: $\Phi$; SI Units: $\text{W}/\text{m}^3$; Dimensions: $\text{ML}^{-1}\text{T}^{-3}$

Diffusivity (mass or heat)

Symbols: $\mathscr{D}, \alpha$; SI Units: $\text{m}^2/\text{s}$; Dimensions: $\text{L}^2\text{T}^{-1}$

Reaction Rate Constant (1st order)

Symbol: $k$; SI Units: $1/\text{s}$; Dimensions: $\text{T}^{-1}$