AP Physics C: Mechanics Questions on Poiseuille's Law

📚 Quick Study Guide

• 🌊 Poiseuille's Law describes the pressure drop of an incompressible and Newtonian fluid in a long cylindrical pipe.
• 📏 The law assumes laminar flow, meaning the fluid flows in smooth layers without turbulence.
• 🌡️ The formula for Poiseuille's Law is: $Q = \frac{\pi R^4 \Delta P}{8 \eta L}$, where:
  • $Q$ is the volumetric flow rate.
  • $R$ is the radius of the pipe.
  • $\Delta P$ is the pressure difference between the ends of the pipe.
  • $\eta$ is the dynamic viscosity of the fluid.
  • $L$ is the length of the pipe.
• 🧪 The key assumptions are: Incompressible fluid, Newtonian fluid, Laminar flow, Constant viscosity, and Rigid pipe.
• 💡 The flow rate is highly sensitive to the radius ($R^4$), so even small changes in radius can significantly affect the flow.

🧪 Practice Quiz

1. A fluid flows through a pipe of radius $R$ and length $L$ with a pressure difference of $\Delta P$. If the radius is doubled, what is the new flow rate $Q'$ in terms of the original flow rate $Q$?
   1. $Q' = 2Q$
   2. $Q' = 4Q$
   3. $Q' = 8Q$
   4. $Q' = 16Q$
2. Which of the following factors does NOT directly affect the flow rate according to Poiseuille's Law?
   1. Fluid density
   2. Pipe radius
   3. Pressure difference
   4. Fluid viscosity
3. A cylindrical pipe has a length of 2 meters and a radius of 0.01 meters. The pressure difference between its ends is 100 Pa, and the fluid's viscosity is 0.001 Pa·s. What is the approximate volumetric flow rate?
   1. $1.96 × 10^{-6} m^3/s$
   2. $3.14 × 10^{-6} m^3/s$
   3. $6.28 × 10^{-6} m^3/s$
   4. $7.85 × 10^{-6} m^3/s$
4. If the length of the pipe is doubled while all other parameters remain constant, what happens to the flow rate?
   1. It doubles
   2. It halves
   3. It remains the same
   4. It quadruples
5. Two pipes have the same length and pressure difference. Pipe A has a radius $R$, and Pipe B has a radius $2R$. What is the ratio of the flow rate in Pipe B to the flow rate in Pipe A ($Q_B/Q_A$)?
   1. 2
   2. 4
   3. 8
   4. 16
6. According to Poiseuille's Law, what is the relationship between fluid viscosity and flow rate?
   1. Flow rate is directly proportional to viscosity.
   2. Flow rate is inversely proportional to viscosity.
   3. Flow rate is independent of viscosity.
   4. Flow rate is proportional to the square of viscosity.
7. In a medical context, Poiseuille's Law helps explain which of the following phenomena?
   1. The speed of nerve impulses
   2. The flow of blood through blood vessels
   3. The diffusion of oxygen in the lungs
   4. The process of osmosis in cells