An arteriole has a radius of 25 m and it is 1000 m long. the viscosity of blood is 3 x 10-3 pa s and its density is 1.055 g cm-3. assume the arteriole is a right circular cylinder. a. assuming laminar flow, what is the resistance of this arteriole?

To solve this problem it is necessary to apply the concepts related to the Hagen-Poiseuille equation law, which is a physical equation for the description of nonideal fluid dynamics, that is the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross-section.  The expression can be extrapolated to the calculation of resistance through an analogy of Ohm's law. Mathematically the equation that describes this phenomenon can be described as,

Where,

R = Resistance

L = Length of pipe

Dynamic viscosity

R = Pipe radius

Our values are given as,

Replacing at the previous equation we have,

Therefore the resistance of this arteriole is