1.A 31' solid circular bar of 2" diameter is fixed to a wall. it is made of aluminum of E=10*10^6. a 30" circular solid 1" diameter aluminum bar is welded to the 2" bar at a 30" centerline perpendicular relative to the other bar per the diagram. a 50 pound load is attached to the end of the second bar at 30". calculate the torque and torsional shearing at the wall.
2.A rectangular channel leading from an upstream lake has a bottom width of 20 ft, bottom slope of 0.0002, a Manning roughness factor of 0.016, a discharge of 403 cfs, and normal depth of 6.24 ft. Then at the downstream end the flow depth is 4.915 ft. Compute and plot the water surface profile upstream of the lake.