Question

Define Poiseuilles Law.

Answer 1

The flow of fluids through an IV catheter can be described by Poiseuille's Law. It states that the flow (Q) of fluid is related to a number of factors: the viscosity (n) of the fluid, the pressure gradient across the tubing (P), and the length (L) and diameter(r) of the tubing.

The Hagen-Poiseuille Equation
$\rho g\frac{h_1}{l}=-(\frac{dp}{dx}+\rho g_x)$

Relationship between head loss and pressure gradient

Hagen-Poiseuille Laminar pipe flow equations
$Q=-\frac{\pi R^4}{8\mu }(\rho g_x+\frac{dp}{dx})$
From Navier-Stokes
If in case double pressure gradient in a horizontal tube - flow doubles
$Q=-\frac{\pi R^4}{8\mu }(-\rho g\frac{h_1}{l})$
$Q=\frac{\pi D^4}{128\mu }\frac{\rho g{h}_1}{l}$
$V=\frac{D^2}{32\mu }\frac{\rho g{h}_1}{l}$ V is average velocity.