Question

The resistivity of blood is related to its hematocrit, the volume fraction of red blood cells in the blood. A commonly used equation relating the hematocrit h to the blood resistivity rho (in Ω⋅m) is rho=1.32/(1−h)−0.79. In one experiment, blood filled a graduated cylinder with an inner diameter of 0.90 cm. The resistance of the blood between the 1.0 cm and 2.0 cm marks of the cylinder was measured to be 198 Ω.
Required:
What was the hematocrit for this blood?

Answer 1

Answer:

$0.35598$

Explanation:

r = Radius = $\dfrac{0.9}{2}=0.45\ \text{cm}$

R = Resistance = $198\ \Omega$

A = Area = $\pi r^2$

l = Length of blood in cylinder = 1 cm

h = Hematocrit of the blood

Resistivity is given by

$\rho=\dfrac{1.32}{1-h}-0.79$

Resistance is given by

$R=(\dfrac{1.32}{1-h}-0.79)\dfrac{l}{\pi r^2}\\\Rightarrow h=1-\dfrac{1.32}{\dfrac{R\pi r^2}{l}+0.79}\\\Rightarrow h=1-\dfrac{1.32}{\dfrac{198\times \pi\times (0.45\times 10^{-2})^2}{0.01}+0.79}\\\Rightarrow h=0.35598$

The hematocrit of the blood is $0.35598$.