Lecture 5 - Law of Poiseuille

Question 1

State assumptions for Poiseuille law

Answer 1

Newtonian fluid (constant viscosity);
* Incompressible;
* Laminar;
* Through a straight pipe (circular cross-section)
where length&raquo_space; diameter;
* Steady (not pulsatile);
* Velocity at wall is zero (no slip at the wall);
* Flow is fully developed (no velocity gradients along
tube); (parabolic velocity profile)

Question 2

Poiseuille Law Equation

Answer 2

Q = (deltaP * pi * r_i ^4)/( 8 * eta * l)

Question 3

Why might the fully developed assumption be invalid?

Answer 3

Velocity profile is not parabolic after bifurcations and curves, and takes some tube length to fully develop

Question 4

Entrance Length equations for laminar and turbulent?

Answer 4

Laminar - Le/D = 0.06 Re

Turbulent - Le/D = 4.4 Re ^1/6

Question 5

WSS for blood ?

Answer 5

tau = deltaP *r / 2l

Question 6

Wall shear as a function of volume flow?

Answer 6

tau = 4etaQ / pi*r_i^3

Question 7

Poiseuille Law in terms of R

Answer 7

R = 8etaL / pi*R_i^4

Question 8

Short and long term effects of WSS on endothelial walls?

Answer 8

Short term - vasomotor tone and flow mediated dilation

Long term - vascular remodelling, endothelial damage
and atherosclerosis

Question 9

Why is in-vivo WSS measurement difficult?

Answer 9

Knowledge of viscosity near the wall is difficult
because of plasma skimming (relative absence of RBC’s near the wall)

WSS is also affected by the vessel diameter. This changes over the heartbeat and is difficult to account for