Law of Laplace — FRCA Primary MCQ

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HardPhysiology - CardiovascularLaw of LaplaceFRCA Primary

A thin-walled spherical chamber initially has transmural pressure P, internal volume V and wall thickness h. It subsequently dilates: transmural pressure increases by 25%, internal volume increases by 72.8%, and wall thickness decreases by 20%. Assuming spherical geometry and application of the law of Laplace, what is the ratio of final to initial mean tensile wall stress?

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Correct answer: E — 1.875

The correct answer is E. For a thin-walled sphere, Laplace's law gives wall tension T = Pr/2. Mean tensile wall stress is tension divided by wall thickness, so sigma = Pr/(2h). A 72.8% increase in volume means V2/V1 = 1.728; because volume is proportional to r cubed, the radius increases by a factor of 1.2. Pressure increases by a factor of 1.25 and thickness falls to 0.8 of its original value. Thus the stress ratio is 1.25 x 1.2/0.8 = 1.875. Option D omits wall thinning, option C omits the radius increase, and option A incorrectly treats the volume ratio as the radius ratio. Option B accounts only for the change in radius.

Reference: Royal College of Anaesthetists. Guide to the FRCA Examination: The Primary, fourth edition. MCQ answer 45(e), 2013. https://www.rcoa.ac.uk/sites/default/files/documents/2025-08/RCoAPrimaryGuide2013%20FOR%20WEBSITE.pdf