In: Physics
While prepping to start an internship at the local hospital you learn that systemic arteries have diameters greater than 10 mm. You know that blood carries charged particles, and you start to wonder how strong a uniform magnetic field would have to be in order to detect the flow of these charges in the blood with a voltmeter that can measure voltage differences down to a millivolt. You assume that the blood flows at a rate of about 10 cm/s
We know that, Q = r4P / 8 L
A v = r4P / 8 L
v = r4P / 8 L A
v = r4P / 8 L ( r2)
v = r2P / 8 L
where, r = radius = 5 x 10-3 m
P = average blood pressure = 1.32 x 104 Pa
= viscosity of blood = 4 x 10-3 Pa.s
v = blood flows speed = 10 cm/s = 0.1 m/s
inserting all these values in above eq,
(0.1 m/s) = (3.14) (5 x 10-3 m)2 (1.32 x 104 Pa) / 8 (4 x 10-3 Pa.s) L
L = (103.6 x 10-6 Pa.m2) / (3.2 Pa.m)
L = 32.3 x 10-6 m
L = 3.23 x 10-5 m