The relationship between velocity and pressure at a stenosis is described by which principle?

The relationship between velocity and pressure at a stenosis is described by which principle?

• A. Bernoulli
• B. Poiseuille
• C. Ohm
• D. Venturi

Answer: (A)

In a constriction, or stenosis, the flow must speed up to keep the same volume of fluid moving per second. Bernoulli’s principle states that along a streamline for steady, incompressible flow, the sum of static pressure and dynamic pressure (½ρv²) remains constant. Therefore, as velocity increases through the narrowed section, the static pressure decreases. This explains why dramatic velocity changes at a stenosis are accompanied by a pressure drop. Poiseuille’s law describes pressure loss in a long, straight, laminar pipe with viscosity and radius fixed; it doesn’t capture how velocity changes with a changing cross-sectional area. Ohm’s-law-like analogies and the Venturi device touch on related ideas, but the fundamental principle governing the velocity–pressure relationship at a stenosis is Bernoulli’s.

In a constriction, or stenosis, the flow must speed up to keep the same volume of fluid moving per second. Bernoulli’s principle states that along a streamline for steady, incompressible flow, the sum of static pressure and dynamic pressure (½ρv²) remains constant. Therefore, as velocity increases through the narrowed section, the static pressure decreases. This explains why dramatic velocity changes at a stenosis are accompanied by a pressure drop.

Poiseuille’s law describes pressure loss in a long, straight, laminar pipe with viscosity and radius fixed; it doesn’t capture how velocity changes with a changing cross-sectional area. Ohm’s-law-like analogies and the Venturi device touch on related ideas, but the fundamental principle governing the velocity–pressure relationship at a stenosis is Bernoulli’s.