Heated air at 1 atm and 25°c is to be transported in a 250 m long circular duct at a rate of 0.45 m/s. if the head loss in the pipe is not to exceed 20m, determine the minimum diameter of the duct.

Aturning operation is performed with following conditions: rake angle of 12°, a feed of 0.35 mm/rev, and a depth of cut of 1.1 mm. the work piece is aluminum alloy 6061 with t6 heat treatment (a16061-t6). the resultant chip thickness was measured to be 1.0 mm. estimate the cutting force, fc. use shear stress of 207 mpa and coefficient of friction on the tool face of 0.6.