QuestionAugust 3, 2025

What will happen to volume flow if the radius of a blood vessel is halved? A Flow is reduced 16 times B Flow is increased 20 times C Flow is decreased by half D Flow is decreased by one-fourth

What will happen to volume flow if the radius of a blood vessel is halved? A Flow is reduced 16 times B Flow is increased 20 times C Flow is decreased by half D Flow is decreased by one-fourth
What will happen to volume flow if the radius of a blood vessel is halved?
A Flow is reduced 16 times
B Flow is increased 20 times
C Flow is decreased by half
D Flow is decreased by one-fourth

Solution
4.1(259 votes)

Answer

(A) Flow is reduced 16 times Explanation 1. Identify the relationship The volume flow rate Q is related to the radius r by **Poiseuille's Law**: Q = \frac{\pi \Delta P r^4}{8 \eta L}, where \Delta P is the pressure difference, \eta is the viscosity, and L is the length of the vessel. 2. Analyze the effect of halving the radius If the radius r is halved, then the new radius r' = \frac{r}{2}. Substitute into the formula: Q' = \frac{\pi \Delta P (\frac{r}{2})^4}{8 \eta L} = \frac{\pi \Delta P r^4}{16 \times 8 \eta L} = \frac{Q}{16}.

Explanation

1. Identify the relationship<br /> The volume flow rate $Q$ is related to the radius $r$ by **Poiseuille's Law**: $Q = \frac{\pi \Delta P r^4}{8 \eta L}$, where $\Delta P$ is the pressure difference, $\eta$ is the viscosity, and $L$ is the length of the vessel.<br /><br />2. Analyze the effect of halving the radius<br /> If the radius $r$ is halved, then the new radius $r' = \frac{r}{2}$. Substitute into the formula: $Q' = \frac{\pi \Delta P (\frac{r}{2})^4}{8 \eta L} = \frac{\pi \Delta P r^4}{16 \times 8 \eta L} = \frac{Q}{16}$.
Click to rate:

Similar Questions