Transport Phenomena I Formula Wall
While taking Transport Phenomena I kept coming back this page. For a more abstract but complete overview of the subject, checkout Continuity and Species Conservation.
Force
\[Force= mass \cdot acceleration =N = kg\cdot\frac{ m}{s^2}\] \[Force=\frac{dP}{dt}=\frac{d}{dt}(\frac{kg\cdot m}{s})=kg\cdot\frac{ m}{s^2}\]Pressure
\[Pressure = \frac{Force}{Area}= Pa = \frac{N}{m^2} = (\frac{kg \cdot m}{s^2})\cdot \frac{1}{m^2} = kg\cdot\frac{1} {m\cdot s^2}\]Momentum
\[Momentum \space(P)=mass\cdot velocity =kg\cdot\frac{m}{s}\]Mass Flow Rate
\[Mass \space Flow= \dot m =\rho \cdot v \cdot A=\frac{kg}{m^3} \cdot \frac{m}{s} \cdot m^2=\frac{kg}{s}\]Mass Flux Rate
\[Mass\space Flux= \frac{Mass \space Flow \space (\dot m)}{Area}=\frac{kg}{m^2 \cdot s}\] \[v \cdot A = \frac{Volume\space (m^3)}{s} \rightarrow \rho \cdot v \cdot A = \frac{Mass\space(kg)}{Volume\space (m^3)}\cdot \frac{Volume\space (m^3)}{s}=\frac{Mass\space(kg)}{s}\]Volumetric Mass Flow Rate
\[Q= \frac{Mass \space Flow \space (\dot m)}{density \space (\rho)}=\frac{\dot m}{\rho}=\frac{kg}{s} \cdot \frac{m^3}{kg} = \frac{m^3}{s}\]Momentum Balance (Although it is actually a Force Balance since $F=\frac{dP}{dt}$)
\[{\frac{d}{dt} \iiint \rho \mathbf{v} dV} = -\iint \mathbf{v} \rho \mathbf{v} \cdot d\mathbf{S} + \iint \tau \cdot d\mathbf{S} + \iiint \rho \mathbf{g} dV + \iiint \mathbf{f} dV\]Gauss’s divergence theorem
\[\iint_S \mathbf{F} \cdot \mathbf{n} \space dS=\iiint_V \nabla \cdot \mathbf{F} \space dV\]Circle Stuff $\bigcirc$
Circumference: $C=2 \pi r$
Area: $A=\pi r^2$