Question

Coronary arteries are responsible for supplying oxygenated blood to heart muscle. Most heart attacks are caused by the narrowing of these arteries due to arteriosclerosis, the deposition of plaque along the arterial walls. A common physiological response to this condition is an increase in blood pressure. A healthy coronary artery. is 3.0 mm in diameter and 4.0 cm in length. ▼ Part A Consider a diseased artery in which the artery diameter has been reduced to 2.6 mm. What is the ratio Qdiseased/Qhealthy if the pressure gradient along the artery does not change?

Answer 1

The flow rate through the diseased artery is 69.8% of the flow rate through the healthy artery when the pressure gradient remains unchanged.

We can use Poiseuille's law to find the ratio of flow rates :

Q = (πΔP R
`^4`) / (8ηL)

where:

Q = the volume flow rate (m^3/s)

ΔP = the pressure difference across the artery (Pa)

R= the radius of the artery (m)

η = the viscosity of blood (Pa·s)

L = the length of the artery (m)

Radius_healthy (R_healthy) = d_healthy / 2 = 0.0015 m

Radius_diseased (R_diseased) = d_diseased / 2 = 0.0013 m

The individual flow rates:

Q_healthy = (πΔP R_healthy
`^4`) / (8ηL_healthy)

Q_diseased = (πΔP R_diseased) /
`^4` (8ηL_diseased)

Q_diseased / Q_healthy = (R_diseased
`^4` / R_healthy
`^4`)

Q_diseased / Q_healthy = (0.0013
`^4` / 0.0015
`^4`) = 0.698

= 69.8%