12 A piece of aluminum tubing must be bent to form part of a

12. A piece of aluminum tubing must be bent to form part of an exhaust system. The pipe is to be bent according to the dimensions shown in the figure below. We want to know the length of pipe needed. Disregard the length needed to smooth and square-off the ends. In computing material length, the mean thickness of the material is used for greater accuracy. That is, find the length of the dotted line running through the center of the pipe. *All radii are given from center-point of the bend to the INSIDE of each bend. 1\'2.75\" i10 R 2.25\" 11.375\" 8.5\"i R 2.25\" R 4.5\" 2\' :45°

Solution

Length = (1\'1.5\"+11.375\"+2\'+8.5\"+1\'2.75\")+(length at for bends)

Length at first bend = 2.25\" × /4 = 1.767\"

Length at second bend = 4.5\" × /4 = 3.534\"

Length at third bend = 3.5\" × /2 = 5.498\"

Length at fourth bend = 2.25\" × 80 × /180 = 3.142\"

So total length of four bends = (1.767+3.534+5.498+3.142)\" = 13.941\" = 1\'1.941\"

Total length = 1\'1.5\"+11.375\"+2\'+8.5\"+1\'2.75\"+1\'1.941\"

Total length = 7\'2.066\"