Consider a thin-walled spherical balloon made of uniform material and having a u
ID: 1939124 • Letter: C
Question
Consider a thin-walled spherical balloon made of uniform material and having a uniform wall thickness. When it is inflated with an internal pressure p, the radius of the sphere is R and the tension in the wall is T per unit length. p = 2T/R Derive the condition of equilibrium: Consider a circular cylindrical tube inflated with an internal pressure p to a radius R. Show that the circumferential tension per unit length, T (the hoop tension), is related to p and R by: p = T/R Resistance to bending of the wall is assumed to be negligible.Explanation / Answer
(a) Use half the ballon as free body, we have
F = 0: p*(R2)-T(2R) = 0 (note the net forcr from pressure equals the pressure by the projected area)
which leads to p = 2T/R
(b) Cut the cylinder along its axis into two part, keeping one part as a free body. We shoud have preesure on the inner surface and tension on the cutting surface.Let L be the length of the cylinder.
F = 0: p*(2RL)-T(2L) = 0 [note again the net forcr from pressure equals the pressure by the projected area L*(2R)]
which leads to p = T/R