Problem $\backslash$# $5$

A fan has blades that are flat plates in the shape of isosceles trapezoids and on the plane perpendicular to the axis of rotation. Dimensions:

Root dimension $\backslash ($ B D$=10\backslash$mathrm$\{$~cm$\}\backslash ).$

Tip dimension $\backslash ($ A C$=4\backslash$mathrm$\{$~cm$\}\backslash ).$

They extend from a radius of $10$ cm at the root, $+026$ cm at the tip. They are attached to a shaft rotating at $120$ rpm $.$ We would like to determine the torque needed to operate the fan. Neglect any friction related to other components of the fan. Air temperature is $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Determine the moment $\backslash ($ d $\backslash$mathrm$\{$~m$\}\backslash )$ at a radius $\backslash ($ r $\backslash ),$ where $\backslash (10\backslash$mathrm$\{$~cm$\}$