Page 118 - Fluid-Structure Interactions Slender Structure and Axial Flow (Volume 1)

100 SLENDER STRUCTURES AND AXIAL FLOW

effect of the third term in (3.99), while ignoring the second, probably reasoning that since
pressurization induces the tensioning, it need not be considered further - thus inventing
the impossible! In reality, the net effect on whirling is zero.
The story of this fallacious patent is charmingly related by Den Hartog (1969), together
with one on an earlier but similarly fallacious patent, this one for preventing buckling
of drill-strings used in oil exploration. It is well known that the very long and slender
drill-rods buckle under the compressive loading required for drilling and they touch the
sidewalls in several places along the length. Then, as the drill-rod rotates and rubs against
the sidewalls, up to 90% of the power is consumed for this non-useful work. The invention
consisted of using a hollow drill-rod and a floating drill-bit, and pumping sludge down
the drill-rod, which would rotate the drill-bit as a turbine, as depicted in Figure 3.18.
Thus, it was thought, the removal of all compressive load from the drill rod would result
in the elimination of all possibility of buckling. However, it should be realized that, to
cause the drill-bit to press hard on the rock and to rotate against it, the pressure p1,
must be substantially larger than p2. Hence, the truth emerges that the drill rod would
buckle just the same due to pressurization, under much the same conditions as the original
system - and perhaps earlier because of the flow effect.

Figure 3.18 The fallacious patent for preventing buckling of drill-strings by the use of a floating
drill-bit, rotating under the action of the flow (Den Hartog 1969).

Returning to a quantitative assessment of pressurization effects, equation (3.98) may
be written in dimensionless terms as