Question

Flow through a coronary artery with a radius of 1um is 4um/sec during a recent bout of exercise. Assuming a constant pressure difference and a change in the radius by half, how would flow compare in that same coronary artery while this individual is resting?

1) Flow would be less, specifically 1 um/sec
2) Flow would be equal at 4 um/sec
3) Flow would be more at 16 um/sec
4) Flow would be less, specifically 1/4 um/sec
5) Flow would be more at 64 um/sec

Answer 1

Flow through a coronary artery will be significantly less, specifically 1/4 um/sec, when the radius is reduced by half according to Poiseuille's Law.

Step-by-step explanation:

When considering how a change in radius affects the flow through a coronary artery, we can refer to Poiseuille's Law, which states that flow rate is proportional to the fourth power of the radius (r^4) when all other factors remain constant. The flow through the artery is initially 4µm/sec with a radius of 1µm. If the radius is halved, the new radius would be 0.5µm. The new flow rate would be proportional to (0.5µm)4 compared to (1µm)4. Since (0.5)4 is 1/16, the new flow rate would be 4µm/sec divided by 16, giving us a flow rate of 0.25µm/sec or specifically, 1/4 um/sec. Therefore, the flow would be significantly less when the individual is resting and the artery's radius is reduced by half.