A bolt is tightened, subjecting its shank to a tensile stress of 80 kpsi and a torsional shear stress of 50 kpsi at a critical point. All of the other stresses are zero. The material is a brittle material with Sut =80 kpsi and Suc =150 kpsi. Find the factor of safety at the critical point by the more conservative failure theory and determine if the bolt will fracture.

Apiping systems consists of 6 m of 6-std type k and 12 m of 4-std type k, both drawn copper tubing. the system conveys ethylene glycol at a rate of 0.013 m3/s. the pressure drop across the system is to be calculated. there are two 90° elbows in the 6-in pipe, a reduction from the 6-in pipe to the 4-in pipe and four 90° elbows in the 4-in pipe. all fittings are soldered (same as flanged) and regular. the inlet and outlet of the system are at the same height.