Transport Phenomena I Formula Wall

June 19, 2025

I took Transport Phenomena without any knowledge of Physics . To really learn the subject and get a feeling of the equations, I broke down the main physical concepts into their most succing definitions and units. Throught the class I kept coming back to the concepts in this page. For a more abstract but complete overview of the subject, checkout Continuity and Species Conservation.

Force

F o r c e = m a s s \cdot a c c e l e r a t i o n = N = k g \cdot \frac{m}{s^{2}}

F o r c e = \frac{d P}{d t} = \frac{d}{d t} (\frac{k g \cdot m}{s}) = k g \cdot \frac{m}{s^{2}}

Pressure

P r e s s u r e = \frac{F o r c e}{A r e a} = P a = \frac{N}{m^{2}} = (\frac{k g \cdot m}{s^{2}}) \cdot \frac{1}{m^{2}} = k g \cdot \frac{1}{m \cdot s^{2}}

Momentum

M o m e n t u m (P) = m a s s \cdot v e l o c i t y = k g \cdot \frac{m}{s}

Mass Flow Rate

M a s s F l o w = \dot{m} = ρ \cdot v \cdot A = \frac{k g}{m^{3}} \cdot \frac{m}{s} \cdot m^{2} = \frac{k g}{s}

Mass Flux Rate

M a s s F l u x = \frac{M a s s F l o w (\dot{m})}{A r e a} = \frac{k g}{m^{2} \cdot s}

v \cdot A = \frac{V o l u m e (m^{3})}{s} \to ρ \cdot v \cdot A = \frac{M a s s (k g)}{V o l u m e (m^{3})} \cdot \frac{V o l u m e (m^{3})}{s} = \frac{M a s s (k g)}{s}

Volumetric Mass Flow Rate

Q = \frac{M a s s F l o w (\dot{m})}{d e n s i t y (ρ)} = \frac{\dot{m}}{ρ} = \frac{k g}{s} \cdot \frac{m^{3}}{k g} = \frac{m^{3}}{s}

Momentum Balance (Although it is actually a Force Balance since $F = \frac{d P}{d t}$ )

\frac{d}{d t} ∭ ρ v d V = - \iint v ρ v \cdot d S + \iint τ \cdot d S + ∭ ρ g d V + ∭ f d V

Gauss’s divergence theorem

\iint_{S} F \cdot n d S = ∭_{V} \nabla \cdot F d V

Circle Stuff $◯$

Circumference: $C = 2 π r$

Area: $A = π r^{2}$