In a thin-walled cylinder under internal pressure, which expression correctly represents the circumferential (hoop) stress?

• A. PD/2t
• B. PR/t
• C. P t / R
• D. P R^2 / t

Answer: (B)

In a thin-walled cylinder under internal pressure, the circumferential (hoop) stress is essentially uniform around the circumference and is given by sigma_hoop ≈ P R / t. Here P is the internal pressure, R is the mean radius of the wall, and t is the wall thickness. The wall must carry the outward force produced by the pressure around the circumference, and this outward force scales with P and R, while thicker walls reduce the stress by the factor 1/t. This is the standard thin-wall result.

If you prefer using diameter, you can write the same relation as PD/2t, since D = 2R; it’s the same value, just a different variable. The other forms misrepresent the physics: Pt/R would imply stress grows with thickness and shrinks with radius in the wrong way, and PR^2/t would introduce a dimensional and physical mismatch since the stress should scale with P and R, not with R^2.