Instrumentation in fluid mechanics: A Pitot–static tube directly senses which types of pressure, and which type does it not measure (being obtained only by difference)?

Introduction / Context:
The Pitot–static tube is a standard device in fluid mechanics and aerodynamics for measuring flow speed in pipes and around bodies. It uses pressure measurements to infer velocity via Bernoulli’s equation. Understanding which pressures are measured directly versus inferred is a core skill for instrumentation questions.

Given Data / Assumptions:

• Pitot–static tube has two ports: an impact (Pitot) opening facing the flow and static side ports.
• Fluid is steady, incompressible, and along a streamline; elevation changes are negligible.
• Bernoulli relation between free stream and stagnation point applies without major losses.

Concept / Approach:
Static pressure acts normal to surfaces and is sampled from side holes aligned to avoid dynamic effects. Total (stagnation) pressure is the pressure when the fluid is brought to rest isentropically at the Pitot opening. Dynamic pressure is not tapped; it is computed as the difference between total and static pressures.

Step-by-Step Solution:
Let p_s = static pressure measured at the lateral ports.Let p_0 = total (stagnation) pressure measured at the forward-facing Pitot opening.Dynamic pressure q = p_0 - p_s.Velocity magnitude V follows V = sqrt(2 * q / rho) where rho is density.

Verification / Alternative check:
A differential manometer connected between the Pitot and static ports reads a head proportional to p_0 - p_s, confirming that the device infers dynamic pressure by subtraction rather than direct measurement.

Why Other Options Are Wrong:

• Static pressure: directly sampled by side ports; hence measured.
• Total pressure: directly sampled by the facing Pitot port; hence measured.
• Both with a single tap: requires two separate ports; a single tap cannot give both simultaneously.
• Vapor pressure: unrelated to Pitot–static operation and not measured.

Common Pitfalls:
Confusing “reading on a differential gauge” with “direct measurement.” The gauge shows the difference, but the tube itself provides static and total; dynamic is derived.

Final Answer:
Dynamic pressure (total minus static)