AAMC FL Practice Exam

What does Poiseuille's Law describe in fluid dynamics?

1. The relationship between pressure and flow rate

2. The relationship between flow rate and vessel radius

3. The relationship between velocity and cross-sectional area

4. The relationship between fluid temperature and pressure

The correct answer is: The relationship between flow rate and vessel radius

Poiseuille's Law describes the relationship between flow rate and vessel radius in a fluid system, particularly in the context of incompressible and Newtonian fluids moving through a cylindrical pipe. According to the law, the flow rate (Q) is directly proportional to the fourth power of the radius (r) of the vessel, which significantly emphasizes the impact of even small changes in radius on the flow rate. This relationship can be mathematically expressed as: \[ Q = \frac{\pi \Delta P r^4}{8 \eta L} \] where \( \Delta P \) is the pressure difference across the length of the pipe, \( \eta \) is the dynamic viscosity of the fluid, and \( L \) is the length of the pipe. This formula highlights how the radius is a critical factor in determining flow rate; for example, doubling the radius would increase the flow rate by a factor of 16, underscoring the importance of vessel diameter in fluid dynamics. The other options, while related to fluid dynamics, do not accurately reflect the core aspect of Poiseuille's Law. The law does include pressure in its expression but specifically outlines how flow rate varies with vessel radius, making the focus on vessel radius essential