An artery supplying heat muscle with blood is occluded to 13.9% of its original radius by a clot. By what percent is the blood flow through this artery reduced.
To determine the percentage by which the blood flow through the artery is reduced, we need to understand the relationship between the radius of an artery and blood flow.
According to the Poiseuille's Law, the blood flow through a vessel is directly proportional to the fourth power of its radius. Mathematically, it can be expressed as:
Flow ∝ r⁴
Where Flow represents the blood flow and r represents the radius of the artery.
Now, let's calculate the reduction in blood flow. Given that the artery is occluded to 13.9% of its original radius, we can consider the radius after occlusion as (100% - 13.9% = 86.1%) of the original radius.
To find the reduction in blood flow, we can compare the original blood flow to the blood flow after the occlusion:
(Flow after occlusion) / (Original flow) = (New radius / Original radius)⁴
Let's denote the reduction in blood flow as R.
R = (Flow after occlusion) / (Original flow) = (New radius / Original radius)⁴
Substituting the given value, we have:
0.861⁴ = R
Calculate the value using a calculator:
0.861⁴ ≈ 0.589
Therefore, the blood flow is reduced to approximately 58.9% (or 41.1% reduction) of its original value.
So, the blood flow through this artery is reduced by approximately 41.1%.