There are two carotid arteries that feed blood to the brain, one on each side of
ID: 1472682 • Letter: T
Question
There are two carotid arteries that feed blood to the brain, one on each side of the neck and head. One patient's carotid arteries are each 11.2 cm long and have an inside diameter of 5.1 mm . Near the middle of the left artery, however, is a 2.0-cm-long stenos is, a section of the artery with a smaller diameter of 3.4 mm . For the same blood flow rate, what is the ratio of the pressure drop along the patient's left carotid artery to the drop along his right artery Express your answer using two significant figures .Explanation / Answer
I'll assume that "near the middle" means at h = 5.6 cm, and
that the density of blood is 1060 kg/m³.
right artery:
p = gh = 1060kg/m³ * 9.8m/s² * -0.056m = -582 Pa
left artery:
p' = ½(v² - v'²) + gh
v' = v(5.1/3.4)² = 2.25v
p' = ½ * 1060kg/m³ * v²(1 - 2.25²) - 582Pa
p' = -2153.125 kg/m³ * v² - 582Pa
We can't get a ratio without the velocity of the blood.
Let's assume that we can ignore the "head" -- the pressure drop due to elevation.
Then
p' / p 2.25² / 1² = 5 : 1 ratio of left drop to right drop ignoring head