A thin-wall cylindrical pressure vessel, of diameter D and wall thickness h, is filled wit...

A thin-wall cylindrical pressure vessel, of diameter D and wall thickness h, is filled with a fluid whose weight density is γ (force per unit volume). The fluid is pressurized until the average pressure in the vessel is p (force per unit area). Assume that the difference in pressure between the top and bottom of the tank is small enough to be neglected. The vessel is supported near its ends on horizontal supports a distance l apart. Design considerations require that a small circular hole be drilled into the vessel at midspan at either the top (point A) or bottom (point B) (Figure P14.11).

Show that if the hole is drilled at point A, the maximum stress at the hole resulting from the fluid and pressure is

σA = (5pD/4h) + (γl2/8h)

and if the hole is drilled at point B,

σB = (5pD/4h) + (γl2/8h)

The weight of the vessel is neglected in estimating the bending stresses at section AB, and the bending stress is assumed to be smaller than the circumferential stress.

FIGURE P14.11