|
58. Problem 14.47 (RHK) A rotor blade 5.27 m long is composed of material of density 4.55 g cm-3 and ultimate tensile strength 446 MN m2. We have to calculate its greatest rotational speed. We can assume that the blade rotates about an axis perpendicular to and through one end of the blade. |
|
Solution: Click For PDF Version Let the cross-sectional area of the blade be
The centripetal force on the blade can be calculated by
integrating contribution of an infinitesimal piece of the blade of width
Tensile stress on the blade is
As the ultimate tensile strength is
Therefore, the greatest possible rotation speed of the blade
is
|
. Length
of the rotor blade
Let
be the
angular speed of the rotor blade.
at a distance x from the end of the blade connected to the rotor over the
length of the blade,
.
That is
,
we have the relation
.