In a Pitot tube, the velocity of the fluid is determined by relating stagnation pressure to static pressure through which principle?

• A. Bernoulli's equation
• B. Archimedes' principle
• C. Hooke's law
• D. Fourier's law

Answer: (A)

The main idea being tested is how energy conservation in fluid flow links pressure to velocity. In a Pitot tube, the fluid is brought to rest at a stagnation point, so its kinetic energy is converted into pressure energy. The static pressure is the pressure of the moving fluid away from the tube. For steady, incompressible flow along a streamline, Bernoulli's equation says that the stagnation pressure equals the static pressure plus the dynamic pressure, which is one-half the fluid density times the velocity squared. The difference between stagnation pressure and static pressure is the dynamic pressure, and from that you can solve for velocity: v = sqrt(2 times (p_stag minus p_static) divided by rho). So the principle used to relate stagnation and static pressures to velocity in a Pitot tube is Bernoulli's equation. The other choices describe unrelated phenomena—Archimedes' principle concerns buoyancy, Hooke's law concerns elastic deformation, and Fourier's law concerns heat conduction—so they don't provide the link between pressure and velocity in this context.