In fluid mechanics, a Pitot tube inserted into a flow is primarily used to measure which quantity at the stagnation point?

Introduction / Context:
Pitot tubes are widely used in aerodynamics, hydraulics, and industrial fluid systems to measure flow conditions. They can be seen on aircraft, inside pipelines, and in wind tunnels. The Pitot tube relies on converting the kinetic energy of the moving fluid into a pressure reading at a stagnation point. This question asks which specific pressure or quantity is measured directly by a Pitot tube inserted into a flow.

Given Data / Assumptions:

• A Pitot tube is placed facing into the flow so that the fluid comes to rest at the tube opening.
• The fluid is assumed incompressible at moderate speeds for simplicity.
• Static pressure, dynamic pressure, and stagnation pressure are defined as in Bernoulli theory.
• We consider the basic form of a Pitot tube, not a combined Pitot static probe.

Concept / Approach:
When fluid enters the mouth of a Pitot tube that faces directly into the flow, it slows down and finally comes to rest at the stagnation point inside the tube. According to Bernoulli equation, the total pressure at this point is the sum of the static pressure and the dynamic pressure of the upstream flow. This total is called stagnation pressure or total pressure. The Pitot tube opening senses this stagnation pressure. Static pressure is usually measured separately by side ports, and dynamic pressure is then obtained as the difference between stagnation and static pressures.

Step-by-Step Solution:
Step 1: Recall that static pressure is the pressure felt by a fluid at rest or measured by a probe aligned parallel to flow without disturbing it significantly. Step 2: Dynamic pressure is given by (1/2) * rho * v^2, where rho is density and v is flow speed, and represents kinetic energy per unit volume. Step 3: Stagnation pressure equals static pressure plus dynamic pressure, and is the pressure at a point where the fluid velocity is brought to zero isentropically. Step 4: A Pitot tube facing the flow creates such a stagnation point at its entrance, so the pressure measured by the Pitot port is the stagnation pressure. Step 5: Dynamic pressure is calculated later by subtracting the separately measured static pressure from the Pitot stagnation pressure.

Verification / Alternative check:
Flow velocity in many practical setups is obtained by combining a Pitot tube with a static pressure tap, forming a Pitot static tube. The manometer connected between the stagnation port and the static port reads the difference, which equals dynamic pressure. That process confirms that the Pitot port itself measures stagnation pressure, not dynamic pressure directly. Aircraft airspeed indicators work in exactly this way.

Why Other Options Are Wrong:
Static pressure only: Static pressure is measured by separate static ports, not by the Pitot port itself. Velocity directly at the stagnation point: At the stagnation point the velocity is zero by definition, so velocity is not measured directly; it is calculated from pressures. Dynamic pressure directly: Dynamic pressure is obtained by subtracting static pressure from stagnation pressure, so it is not sensed directly by a single Pitot opening.

Common Pitfalls:
Students often confuse dynamic and stagnation pressure because both appear together in Bernoulli equation. It is helpful to remember that Pitot tubes stop the flow locally, so they must sense the combined effect of static and dynamic pressures, which is the stagnation pressure. Dynamic pressure is always a derived quantity, not something measured directly by a single simple port.

Final Answer:
A Pitot tube primarily measures the stagnation pressure (total pressure) of the flow at the stagnation point.