In order to reduce the bending moment in the cantilever beamAB, a cable and counterweightare permanently attached at endB. Determine the magnitude of the counterweight for which themaximum absolute value of the bending moment in the beam is as small as possible and thecorresponding value ofjMjmax. Consider (a) the case when the distributed load is permanentlyapplied to the beam(b) the more general case when the distributed load may either be applied orremoved.

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.