Question

Pitot tube is used for measuring:

• A. Total fluid velocity
• B. Local fluid velocity
• C. Average velocity
• D. Maximum fluid velocity

Hint:

Think of a Pitot tube as a point sensor. It tells you how fast the fluid is moving right where you put it. To get average or maximum velocities, you'd need multiple measurements or additional assumptions about the flow profile.

Answer 1

The Correct Option is B

Step 1: Understand the principle of a Pitot tube.
A Pitot tube is a pressure measurement instrument used to determine the velocity of a fluid flow. It works by measuring the stagnation pressure (also known as total pressure) and comparing it to the static pressure of the fluid.
Step 2: Explain how velocity is derived from pressure measurements.
According to Bernoulli's principle for a steady, incompressible flow along a streamline, the total pressure \( P_t \) is the sum of the static pressure \( P_s \) and the dynamic pressure \( \frac{1}{2} \rho v^2 \), where \( \rho \) is the fluid density and \( v \) is the fluid velocity. \[ P_t = P_s + \frac{1}{2} \rho v^2 \] A Pitot tube typically has two openings: one that faces directly into the flow to measure the stagnation pressure and another that is parallel to the flow to measure the static pressure. By measuring the difference between these two pressures (\( P_t - P_s = \frac{1}{2} \rho v^2 \)), the local fluid velocity \( v \) at the point where the Pitot tube is placed can be determined: \[ v = \sqrt{\frac{2(P_t - P_s)}{\rho}} \]
Step 3: Differentiate between local, average, total, and maximum velocity.
Local fluid velocity: The velocity of the fluid at a specific point in the flow field.
Average velocity: The mean velocity of the fluid across a given cross-section of the flow. It is typically calculated by integrating the local velocities over the area and dividing by the area.
Total fluid velocity: This term is not commonly used as a distinct type of velocity in the context of Pitot tube measurement. The Pitot tube measures the magnitude of the velocity vector at a point.
Maximum fluid velocity: The highest velocity within a flow field, which often occurs at a specific location (e.g., at the center of a pipe in laminar flow).

Step 4: Determine what a Pitot tube directly measures.
A Pitot tube, when placed at a specific point in a fluid flow, measures the stagnation and static pressures at that point. Using these measurements, the velocity calculated is the velocity of the fluid at that particular location. Therefore, a Pitot tube measures the local fluid velocity.
Step 5: Evaluate the given options.
Option 1 (Total fluid velocity): Incorrect, as the Pitot tube measures velocity at a point.
Option 2 (Local fluid velocity): Correct, as explained above.
Option 3 (Average velocity): Incorrect; average velocity requires measurements across the entire flow area and integration.
Option 4 (Maximum fluid velocity): Incorrect; the Pitot tube measures the velocity at its specific location, which may or may not be the maximum velocity in the flow field.

Step 6: Select the correct answer.
Pitot tube is used for measuring local fluid velocity.