AP Physics C: Bernoulli's Equation: Sample Problems and Tests

📚 Quick Study Guide

• 🌊 Bernoulli's Equation: Describes the relationship between pressure, velocity, and height of a fluid in a moving streamline. Mathematically, it's expressed as: $P + \frac{1}{2}\rho v^2 + \rho gh = constant$, where $P$ is pressure, $\rho$ is fluid density, $v$ is fluid velocity, $g$ is acceleration due to gravity, and $h$ is height.
• 💨 Assumptions: Bernoulli's equation is applicable under certain assumptions: the fluid is incompressible, the flow is steady (not changing with time), the fluid is non-viscous (no internal friction), and the flow is along a streamline.
• 📏 Applications: Used in various real-world scenarios, including aircraft lift, fluid flow in pipes, and measuring fluid velocities using devices like Venturi meters.
• 📐 Venturi Effect: The reduction in fluid pressure that results when a fluid flows through a constricted section (or choke) of a pipe. This is a direct application of Bernoulli's principle.
• 💡 Problem-Solving Tips: Identify known quantities, choose two points along a streamline, apply Bernoulli's equation between these points, and solve for the unknown. Be careful with units!

🧪 Practice Quiz

1. Which of the following is NOT an assumption for Bernoulli's equation?
   1. A) Incompressible fluid
   2. B) Steady flow
   3. C) Viscous fluid
   4. D) Flow along a streamline
2. Bernoulli's equation is based on the principle of:
   1. A) Conservation of mass
   2. B) Conservation of energy
   3. C) Conservation of momentum
   4. D) Conservation of charge
3. What does the term $\frac{1}{2}\rho v^2$ represent in Bernoulli's equation?
   1. A) Pressure energy
   2. B) Potential energy
   3. C) Kinetic energy per unit volume
   4. D) Thermal energy
4. In a Venturi meter, where is the fluid velocity the highest?
   1. A) At the widest section
   2. B) At the narrowest section
   3. C) At the inlet
   4. D) At the outlet
5. If the velocity of a fluid increases, what happens to its pressure according to Bernoulli's equation (assuming height is constant)?
   1. A) Pressure increases
   2. B) Pressure decreases
   3. C) Pressure remains constant
   4. D) Pressure oscillates
6. Which of the following is an application of Bernoulli's principle?
   1. A) Hydraulic brakes
   2. B) Aircraft lift
   3. C) Ohm's law
   4. D) Archimedes' principle
7. A fluid flows through a pipe of varying cross-sectional area. At point A, the area is larger than at point B. Where is the pressure greater?
   1. A) Point A
   2. B) Point B
   3. C) Pressure is the same at both points
   4. D) Cannot be determined