Question

5. The blood speed in a normal segment of a horizontal artery is 0.10 m/s. An abnormal segment of the artery is narrowed down by an arteriosclerotic plaque to one-fourth 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 1

here we assume region 1 contains narrowed area and region 2 contains normal area

Pressure difference between two horizontal artery is given by bernouilli equation

P2-P1 = 1/2*rho*V1^2 - 1/2*rho*V2^2

since the flow rate of blood same at two point

by using equation of continuity

A1V1 = A2V2

V1 = A2V2/A1

A1 = 1/4A2

substitue these values in bernouilli equation

P2-P1 = 1/rho*V1^2 - 1/2*rho*V2^2

P2-P1 = 1/2*rho*(A2V2/A1)^2 - 1/2*rho*V2^2

P2-P1 = 1/2*rho16V2^2 - 1/2*rho*V2^2

P2-P1 = 1/2*rho*V2^2(16-1)

here V2 = 0.10 , rho = 1060 kg/m^3

P2-P1 = 1/2 * 1060 * (0.10)^2 * 15

P2-P1 = 79.5 Pa