Stagnation concepts in fluid flow:\n“The pressure at a stagnation point is always low.” State whether this statement is correct.

Introduction / Context:
A stagnation point is where the local fluid velocity relative to the body becomes zero. Bernoulli’s principle (for incompressible, inviscid regions) shows that as kinetic energy per unit weight converts to pressure head, the static pressure rises. Thus, stagnation pressure is the highest pressure felt by a probe aligned with the flow (ignoring viscous losses within the probe).

Given Data / Assumptions:

• Subsonic, incompressible flow near a body.
• Negligible height change locally.
• Use of Bernoulli along a streamline into the stagnation point.

Concept / Approach:
Bernoulli: p/ρg + v^2/(2g) ≈ constant along a streamline (inviscid). At a stagnation point, v → 0, so p_stag = p_static + ρ v^2/2. Therefore, stagnation pressure exceeds the local static pressure, not lower. In compressible flows, total pressure includes compressibility effects but still represents a maximum for isentropic deceleration.

Step-by-Step Solution:

Verification / Alternative check:
Pitot tubes measure stagnation pressure, then subtract static pressure to yield dynamic pressure; the reading is positive, reinforcing that stagnation pressure is higher.

Why Other Options Are Wrong:

• Agree: Contradicts Bernoulli and standard measurements.
• Only true in turbulent / high Mach: Neither turbulence nor Mach alone reverses the pressure rise on deceleration to zero speed.

Common Pitfalls:
Confusing base pressure in separated wakes (often low) with stagnation pressure at the nose; mixing static and total (stagnation) pressure terminology.

Final Answer:
Disagree