A cylindrical stream of water falls freely through air. If the radius of the cylinder is r, atmospheric pressure is p0, and surface tension of water is S, what is the pressure just inside the cylindrical surface?

p0 + 2S/r
p0 + 4S/r
p0 + S/r
p0 + 3S/r

Correct answer: p0 + S/r

Solution

The Young-Laplace equation gives excess pressure as S*(1/R1 + 1/R2). For a cylindrical surface: R1 = r (radius of cylinder), R2 = infinity (curvature along the axis). So delta_P = S/r + S/infinity = S/r. Hence P_inside = p0 + S/r.

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