Taking all the Poiseuille flow approximations except that the fluid is Newtonian, determine the velocity profile and flow rate assuming blood is a Bingham plastic fluid based on the shear stress relationship below. Plot the velocity profile of a Newtonian fluid, a pseudoplastic fluid, and a Bingham plastic fluid. How do they differ? Determine the flow rate assuming a Bingham plastic fluid.

${}_{rz}=-\frac{du}{dr}+{}_y$