Solved Examples of Venturi Meter Problems in AP Physics C

📚 Quick Study Guide

🔍 Venturi meters are used to measure the flow rate of a fluid in a pipe.

🧪 Bernoulli's Equation: States that for an ideal fluid, the sum of pressure energy, kinetic energy, and potential energy per unit volume is constant: $P_1 + \frac{1}{2}\rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho g h_2$.

💧 Continuity Equation: States that for an incompressible fluid, the product of the cross-sectional area and the fluid velocity is constant: $A_1v_1 = A_2v_2$.

💡 Venturi Effect: The pressure of a fluid decreases as the velocity of the fluid increases.

📐 Flow Rate (Q): The volume of fluid that passes a point per unit time: $Q = Av$, where A is the cross-sectional area and v is the velocity.

📏 Pressure Difference: The difference in pressure between two points in the Venturi meter is related to the fluid velocity and can be measured using a manometer.

📝 Key Assumptions: Incompressible fluid, steady flow, and negligible viscosity.

Practice Quiz

1. A Venturi meter is used to measure the flow rate of water in a pipe. The diameter of the pipe is 10 cm, and the diameter of the throat is 5 cm. If the pressure difference between the pipe and the throat is 5000 Pa, what is the velocity of the water in the pipe? (Assume the density of water is 1000 kg/m³)
   1. 0.5 m/s
   2. 1.0 m/s
   3. 1.5 m/s
   4. 2.0 m/s
2. Which principle is the Venturi meter based upon?
   1. Pascal's Principle
   2. Archimedes' Principle
   3. Bernoulli's Principle
   4. Newton's Laws of Motion
3. What happens to the fluid pressure as it passes through the constriction (throat) of a Venturi meter?
   1. Increases
   2. Decreases
   3. Remains the same
   4. Fluctuates randomly
4. A Venturi meter has a wider section with area $A_1$ and a narrower section with area $A_2$. If the fluid velocity at $A_1$ is $v_1$, what is the fluid velocity at $A_2$?
   1. $v_1$
   2. $(A_1/A_2)v_1$
   3. $(A_2/A_1)v_1$
   4. $(A_1 + A_2)v_1$
5. Which of the following assumptions is NOT typically made when analyzing a Venturi meter?
   1. Incompressible fluid
   2. Steady flow
   3. Viscous fluid
   4. Negligible viscosity
6. What does the continuity equation state about the relationship between area and velocity in an incompressible fluid flow?
   1. Area and velocity are directly proportional.
   2. Area and velocity are inversely proportional.
   3. Area and velocity are independent of each other.
   4. The product of area and velocity is always zero.
7. If the pressure difference measured by a Venturi meter increases, what does this indicate about the flow rate?
   1. The flow rate decreases.
   2. The flow rate increases.
   3. The flow rate remains constant.
   4. The flow rate becomes zero.