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Bernoulli Principle — FRCA Primary MCQ

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ModeratePhysics & Clinical MeasurementBernoulli PrincipleFRCA Primary

An ideal incompressible fluid flows steadily along a horizontal tube that contains a constriction. Compared with the wider upstream section, which statement correctly describes the fluid at the narrowest point?

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Correct answer: A — Velocity is higher, static pressure is lower, and total pressure is unchanged

Explanation lettering: E = shown as B · D = shown as C · C = shown as D · B = shown as E

A is correct. Conservation of mass requires velocity to increase as an incompressible fluid enters a smaller cross-sectional area. For steady, inviscid flow along a horizontal streamline, Bernoulli's equation is P + ½ρv² = constant. The increased kinetic-energy term at the constriction is therefore accompanied by a fall in static or lateral pressure, while total pressure remains unchanged. This relationship underlies the Venturi effect and gas entrainment devices. B incorrectly predicts increased total pressure without an energy source. C describes a loss of total pressure, which would reflect viscous or turbulent energy dissipation rather than the ideal Bernoulli model. D reverses the continuity relationship. E incorrectly states that static pressure rises as velocity increases.

Reference: Royal College of Anaesthetists. Guide to the FRCA Examination: The Primary, fourth edition, section 'Bernoulli’s principle and Venturi effect', p. 186, 2013. https://www.rcoa.ac.uk/sites/default/files/documents/2025-08/RCoAPrimaryGuide2013%20FOR%20WEBSITE.pdf