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 270 Ω.

Answer 1

0.47361

Step-by-step explanation:

L = Length of cylinder = 1 cm

d = Diameter of cylinder = 0.9 cm

r = Radius of cylinder =
`(d)/(2)=(0.9)/(2)=0.45\ cm`

h = Hematocrit

A = Area =
`\pi r^2`

The resistivity of blood is given by

`\rho=(1.32)/(1-h)-0.79`

The resistivity of a material is given by

`R=\rho(L)/(A)\\\Rightarrow R=(1.32)/(1-h)-0.79* (0.01)/(\pi 0.0045^2)\\\Rightarrow h=1-(1.32)/((AR)/(L)+0.79)\\\Rightarrow h=1-(1.32)/((\pi 0.0045^2* 270)/(0.01)+0.79)\\\Rightarrow h=0.47361`

The hematocirt of the blood is 0.47361