Air (density 1.2 kg/m³) flows through a duct at 50 m/s. A static pressure tap perpendicular to the flow reads 100,000 Pa. A Pitot tube facing into the flow is installed at the same location. What pressure does the Pitot tube read?
A100,000 Pa — the Pitot tube measures static pressure, same as the wall tap
B101,500 Pa — stagnation pressure equals static pressure plus dynamic pressure (½ρV² = ½ × 1.2 × 2500 = 1,500 Pa)
C97,000 Pa — the Pitot tube measures dynamic pressure only, which is less than static pressure
D50,000 Pa — dynamic pressure is half the static pressure at this flow speed
Stagnation pressure = static pressure + dynamic pressure = P_static + ½ρV² = 100,000 + ½(1.2)(50²) = 100,000 + 1,500 = 101,500 Pa. The Pitot tube brings the flow to rest at its tip, converting all kinetic energy to pressure. The static tap measures pressure without decelerating the flow. The difference (1,500 Pa) is the dynamic pressure. This is exactly how airspeed is measured: V = √(2(P_stag − P_static)/ρ). Option A is the key misconception to avoid — Pitot tubes and static taps measure fundamentally different quantities.
Question 2 Multiple Choice
A student argues: 'In very fast-moving air, all the pressure has been converted to kinetic energy, so the static pressure must be nearly zero.' What is the fundamental error in this reasoning?
AThe student is correct — at very high velocities, static pressure approaches zero as kinetic energy dominates
BThe error is that static pressure is always present in a moving fluid; dynamic pressure represents additional kinetic energy that becomes pressure only when the flow decelerates to rest — the two coexist at all nonzero velocities
CThe error is that kinetic energy and pressure are measured in different units and cannot be compared directly
DThe student is almost correct, but static pressure approaches zero only at supersonic speeds, not subsonic speeds
Static pressure is an inherent property of the fluid related to molecular motion — it is always present whether the fluid moves or not. Dynamic pressure ½ρV² is the kinetic energy per unit volume of the bulk flow, and it represents additional pressure that appears *only when the flow is brought to rest* (at a stagnation point). In a moving fluid, both exist simultaneously: the static pressure acts on surfaces parallel to the flow, and the stagnation pressure (static + dynamic) acts on surfaces facing the flow. Bernoulli's equation says their sum is conserved along a streamline — not that one replaces the other.
Question 3 True / False
Dynamic pressure is a type of pressure that moving fluids exert in the direction perpendicular to the flow, in addition to the static pressure they exert on most surfaces.
TTrue
FFalse
Answer: False
Dynamic pressure ½ρV² is not a separate force on surfaces perpendicular to flow — it is the kinetic energy per unit volume of the bulk motion. It only manifests as an actual pressure increase on surfaces that bring the flow to rest (stagnation surfaces, like the tip of a Pitot tube or the leading edge of an airfoil). On surfaces parallel to the flow (static pressure taps), only static pressure acts. Calling dynamic pressure a 'type of pressure on perpendicular surfaces' confuses the energy quantity with the stagnation effect.
Question 4 True / False
In ideal (inviscid, incompressible) flow along a streamline, a region where the fluid moves faster has lower static pressure than a region where it moves slower.
TTrue
FFalse
Answer: True
This is a direct statement of Bernoulli's equation: P + ½ρV² = constant along a streamline. If velocity increases (½ρV² increases), static pressure P must decrease to keep the sum constant. This principle explains lift on airfoils (faster flow over the curved top surface lowers pressure above the wing), flow through constrictions (higher velocity in a narrowed pipe means lower static pressure — the Venturi effect), and many other phenomena. The key qualifier is 'along a streamline' for inviscid, incompressible, steady flow.
Question 5 Short Answer
Why does a Pitot tube measure stagnation pressure rather than static pressure, and how is fluid velocity derived from these two measurements?
Think about your answer, then reveal below.
Model answer: A Pitot tube faces directly into the oncoming flow. The fluid approaching the tube's opening is decelerated to zero velocity at the tip — a stagnation point. At a stagnation point, all kinetic energy converts to pressure, so the pressure rises from static pressure to stagnation pressure (P_stag = P_static + ½ρV²). A separate static port (a tap perpendicular to the flow, where fluid is not decelerated) measures static pressure alone. The velocity is then derived from the difference: V = √(2(P_stag − P_static)/ρ). The two measurements together isolate the dynamic pressure ½ρV², from which velocity follows.
This measurement strategy directly embodies the distinction between static and dynamic pressure. The Pitot-static system — combining a forward-facing stagnation tube with a static port — is the standard airspeed measurement device in aviation. The same principle operates in industrial flow meters (Pitot probes in ducts) and in research (hot-wire anemometry aside, Pitot tubes remain a standard for velocity measurement). The key insight is that you need both measurements to isolate V; neither alone is sufficient.