Two vessels are compared as shown belorv. Assuming constant pressure along both the vessels and linear flow pattern, what will be the flow across the vessel 1 compared to vessel 2?
**Core Concept**
The question is testing the understanding of the relationship between vessel radius, blood pressure, and flow rate, as described by Poiseuille's law. This law states that flow rate is directly proportional to the fourth power of the radius of the vessel.
**Why the Correct Answer is Right**
According to Poiseuille's law, flow rate (Q) is given by the equation: Q ∝ r^4, where r is the radius of the vessel. This means that a small increase in the radius of the vessel results in a disproportionately large increase in the flow rate. In the given scenario, vessel 1 has a larger radius than vessel 2, so the flow across vessel 1 will be significantly higher than vessel 2.
**Why Each Wrong Option is Incorrect**
**Option A:** This option is not a valid comparison, as it does not provide any information about the relationship between the two vessels.
**Option B:** This option suggests that the flow across the two vessels will be equal, which contradicts Poiseuille's law. A larger radius vessel will always have a higher flow rate than a smaller radius vessel.
**Option C:** This option is incorrect because it does not provide a valid comparison between the two vessels. To determine the relative flow rates, we need to know the relationship between the radii of the two vessels.
**Option D:** This option suggests that the flow across vessel 1 will be lower than vessel 2, which is the opposite of what is expected based on Poiseuille's law.
**Clinical Pearl / High-Yield Fact**
A 10% increase in the radius of a vessel can result in a 400% increase in flow rate, highlighting the significant impact of vessel radius on blood flow.
**Correct Answer:** . Flow across vessel 1 will be significantly higher than vessel 2 due to the larger radius.