The blood speed in a normal segment of a horizontal artery is 0.13 m/s. An abnor

Question

The blood speed in a normal segment of a horizontal artery is 0.13 m/s. An abnormal segment of the artery is narrowed down by an arteriosclerotic plaque to one-third the normal cross-sectional area. What is the difference in blood pressures between the normal and constricted segments of the artery? (The density of the blood is 1060 kg/m³, answer in Pa)

Numerical answers must be typed to the most accurate value.
Numerical answers within 3% of the actual answer are counted as correct.
To avoid rounding errors in calculations, use at least three (3) significant figures for numerical answers.

Explanation / Answer

Using Bernoulli's principle:

v^2/2 +P/rho = cst

if the area decreases to 1/3 its original amount, then the velocity increases by a factor of 3 (continuity equation), so we have

(0.13 m/s)^2/2 + P1/rho = P2/rho +(0.39m/s)^2/2
P1-P2=rho/2(0.39^2-0.13^2)
P1- P2 = (1060 /2) * (0.39^2-0.13^2))
P1- P2 = 71.656 Pa

Difference in blood pressures between the normal and constricted segments of the artery, = 71.656 Pa

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