Question

The femoral artery is the large artery that carries blood to the leg. What is the resistance of a $20cm$ long column of blood in a 1.0-cm-diameter femoral artery? The conductivity of blood isrole="math" localid="1649056084708" $0.63{\Omega }^{-1}{\mathrm{m}}^{-1}.$

Short answer

The resistance of a $20cm$long column of blood in a$1.0cm$ diameter femoral artery is$4.04K\Omega$.

Step-by-step solution

Given Information 

Column of blood length$=20cm$

Column of blood $=1.0cm$

The conductivity of blood is$=0.63{\Omega }^{-1}{\mathrm{m}}^{-1}$

Explanation 

If the area and length of the cross-section are given, and a constant is chosen, such as resistivity, $\rho$, or conductivity, $\sigma$, the resistance will be:

$R=\rho \frac{L}{A}=\frac{L}{\sigma A}$

The area is a circle, we can substitute $A=\frac{\pi D^2}{4}$, thus finding

$R=\frac{4L}{\sigma \pi D^2}$

Substitute the expression,

role="math" localid="1649056583426" $R=\left(\frac{4\times 0.2m}{0.63{\Omega }^{-1}{\mathrm{m}}^{-1}\times \pi \times 0.01m^2}\right)$

role="math" localid="1649056713816" $=4.04\mathrm{k}\Omega$

Final Answer

Hence, the resistance of a$20cm$long column of blood in a$1.0cm$ diameter femoral artery is$4.04\mathrm{k}\Omega .$