Question

Determine the ratio between the cross-sectional areas of two blood vessels, assuming that the voltage ratio induced in identical magnetic flow probes is equal to 2:4 and the ratio of blood flows velocity through these vessels is 3:7. (Hint: the blood flow velocity V = (B) ∗ (L) ∗ (u), V is the voltage measured by the electrodes l is the diameter of the blood vessel B is the magnitude of the magnetic field. The electrodes, magnetic field and the blood flow direction are perpendicular to each other)

Answer 1

Cosider a blood vessel with L is the diameter and the blood is flowing through a uniform velocity, ie,

V=B X L X U

where the blood vesselis placed in a uniform magnetic field that is 'B' that is perpendicular to the direction of blood flow and 'L' is the diameter of the blood vessel and 'U ' is the voltage measured by the electrodes

Here the cross section can be calculated as :

Consider the cross section of blood vessel as a circular area

Then area of the circle is $\small \pi r$ 2 ,and the diameter of the blood vessel is 'L' so the radius is 1/2 of 'L'

Thus the area of cross section "A" = $\small \pi$ x (1/2L)²

Here $\small \pi$ is a constant,that is 3.14