Question

Determine the pressure drop along a venule of the length L and the radius R, if the viscosity of blood is ƞ and the speed of blood at the central layer of the venule is v0

Answer 1

According to the Hagen–Poiseuille equation (see https://en.wikipedia.org/wiki/Hagen–Poiseuille_equation) the pressure drop is given as follows:

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

where $Q$ is the volumetric flow rate. By definion, for a cylindrical pipe with only velocity component along the pipe, $Q$ is given as follows:

$$Q = v_0A$$

where $A = \pi R^2$ is the cross-sectional area of the pipe. Substituting the expression for $Q$ in the first formula, obtain:

$$\Delta P = \frac{8 \eta L v_0\pi R^2}{\pi R^4} = \frac{8 \eta L v_0}{R^2}$$

Answer. $\Delta P = \frac{8 \eta L v_0}{R^2}$