AP Physics C: Mechanics Questions on Venturi Meters with Answers

📚 Quick Study Guide

• 🌊 Venturi Meter: A device used to measure the flow rate of a fluid in a pipe.
• 📏 Principle: Based on Bernoulli's principle and the continuity equation.
• 🧮 Continuity Equation: $A_1v_1 = A_2v_2$, where $A$ is the cross-sectional area and $v$ is the fluid velocity.
• ⚡ Bernoulli's Equation: $P_1 + \frac{1}{2}\rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho gh_2$, where $P$ is pressure, $\rho$ is density, $v$ is velocity, $g$ is acceleration due to gravity, and $h$ is height.
• ⬇️ Simplified Bernoulli's Equation (horizontal pipe): $P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$
• 📐 Flow Rate (Q): $Q = Av$, where $A$ is area and $v$ is velocity. Commonly measured in $m^3/s$.
• 💡 Pressure Difference: The pressure difference between the wider and narrower sections of the Venturi meter is used to determine the fluid's velocity and flow rate.

🧪 Practice Quiz

1. A Venturi meter is used to measure the:

   1. Fluid's temperature
   2. Fluid's density
   3. Fluid's flow rate
   4. Fluid's viscosity

2. What principle is the Venturi meter based on?

   1. Archimedes' principle
   2. Pascal's principle
   3. Bernoulli's principle
   4. Newton's laws of motion

3. In a horizontal Venturi meter, where is the fluid velocity the highest?

   1. At the widest section
   2. At the narrowest section
   3. Velocity is constant
   4. At the midpoint

4. What happens to the pressure at the narrow section of a Venturi meter compared to the wider section?

   1. Pressure is higher
   2. Pressure is lower
   3. Pressure is the same
   4. Pressure oscillates

5. If the area of the narrow section of a Venturi meter is halved, what happens to the fluid velocity there (assuming constant flow rate)?

   1. It is halved
   2. It doubles
   3. It remains the same
   4. It quadruples

6. Which equation relates the areas and velocities of a fluid in a Venturi meter?

   1. $P = F/A$
   2. $A_1v_1 = A_2v_2$
   3. $F = ma$
   4. $V = IR$

7. A Venturi meter is horizontal. If the pressure difference between the wide and narrow sections is zero, what can you conclude about the fluid's velocity?

   1. The fluid is stationary
   2. The fluid velocity is infinite
   3. The fluid velocity is decreasing
   4. The fluid velocity is increasing