Poiseuille's Law

#Physics
"Poy-zai"
For laminar flow. Analogous to Ohm's Law

$\displaystyle Q=\frac{\pi r^{4}\Delta P}{8\eta L}$

• $\displaystyle Q$ is the volumetric flow rate $\displaystyle \left( \mathrm{\frac{m^{3}}{s}} \right)$
• $\displaystyle r$ is the tube radius
• $\displaystyle \Delta P$ is the pressure gradient between the two sides of the tube
• $\displaystyle \eta$ is the fluid viscosity
• $\displaystyle L$ is the tube length

$\displaystyle R=\frac{\Delta P}{Q}=\frac{8\eta L}{\pi r^{4}}$

• $\displaystyle R$ is the resistance from the tube the fluid experiences
• Analogous to resistance in circuits where $\displaystyle R=\frac{\rho L}{A}$

Relationship/Love Analogy

(credit: Tracy)
One can think of the transmittance of love as like the flow of fluid through a pipe:

$\displaystyle \Delta P=QR$

• $\displaystyle P$ (pressure differential between two ends bodies of water) is the effort one puts into a relationship
• $\displaystyle Q$ (volumetric flow rate) is the total flow of love the lover receives
• $\displaystyle R$ (resistance) is the resistance to the romantic's love by the receiver

$\displaystyle R\sim \frac{\eta L}{A}$

• $\displaystyle R$ (resistance) is again the resistance to the romantic's love by the receiver
• $\displaystyle \eta$ (viscosity of the fluid) is the medium of communication (speech, calls, texts, body language, quality time, physical touch, gifts, art, music, memes, shitposts, etc.)
• $\displaystyle L$ (length of pipe) is the proximity of the lovers to each other (either physically or emotionally, RIP long distance relationships)
• $\displaystyle A$ (cross-sectional area of pipe) is how receptive to being loved the receiver is