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,
[tex]R = \frac{8\mu L}{\pi R^4}[/tex]
Where,
R = Resistance
L = Length of pipe
[tex]\mu =[/tex] Dynamic viscosity
R = Pipe radius
Our values are given as,
[tex]\mu = 3*10^{-3}Pa\cdot s[/tex]
[tex]L = 1000*10^{-6}m[/tex]
[tex]R = 25*10^{-6}m^4[/tex]
Replacing at the previous equation we have,
[tex]R = \frac{8(3*10^{-3})(1000*10^{-6})}{\pi (25*10^{-6})^4}[/tex]
[tex]R = 1.9556*10^{13}Pa\cdot s/m^3[/tex]
Therefore the resistance of this arteriole is [tex]1.9556*10^{13}Pa\cdot s/m^3[/tex]
