Blood is flowing through an aorta of 1.0 cm diameter at an average velocity of 5
ID: 1919970 • Letter: B
Question
Blood is flowing through an aorta of 1.0 cm diameter at an average velocity of 50 cm/s. The mean pressure is 100 mm Hg, The blood enters a stenosis where the aortic diameter is 0.5 cm. What is the appropriate pressure at the point of maximum stenotic narrowing?
What would the pressure be if the patient exercised and raised their upstream mean velocity to four times normal (200 cm/s)? let blood density be 1.056 g/cc, and let 1 g/cm-sec^2 = 7.5x10^-4 mm Hg
Explanation / Answer
from continuity equations; A1 *v1 = A2 *v2 => (pi*1^2/4) *50 = (pi*0.5^2/4)*v2 => v2 = 200 cm/s P1 = 100 mm of Hg = 13332.237 N/m^2 p = density of blood = 1.056 g/cc = 1056 kg/m^3 v1 = 50 cm/s = 0.5 m/s v2 = 200 cm/s = 2 m/s from Bernoulli's equation; P1 + p*g*y1 + 0.5*p*v1^2 = P2 + p*g*y2 + 0.5*p*v2^2 => 13332.237 + (1056* 9.8*y) + (0.5*1056 *0.5^2) = P2 + (1056*9.8*y) + (0.5*1056 *2^2) => P2 = 11352.237 N/m^2 = 85.149 mm of Hg