A ductile AISI 1030 hot-rolled steel bar is stressed. Using the distortion-energy and maximum-shear-stress theories determine the factors of safety for the following plane stress states: a) σx = 20 ksi, σy = 15 ksi
b) σx = 15 ksi, σy = −20 ksi
c) σx = 20 ksi, τxy = −15 ksi
d) σx = −10 ksi, σy = 15 ksi, τxy = −10 ksi
e) σx= −24 ksi, σy = −20 ksi, τxy = −15 ks

Apump is used to circulate hot water in a home heating system. water enters the well-insulated pump operating at steady state at a rate of 0.42 gal/min. the inlet pressure and temperature are 14.7 lbf/in.2, and 180°f, respectively; at the exit the pressure is 60 lbf/in.2 the pump requires 1/15 hp of power input. water can be modeled as an incompressible substance with constant density of 60.58 lb/ft3 and constant specific heat of 1 btu/lb or. neglecting kinetic and potential energy effects, determine the temperature change, in °r, as the water flows through the pump.

Air is compressed isentropically from an initial state of 300 k and 101 kpa to a final temperature of 1000 k. determine the final pressure using the following approaches: (a) approximate analysis (using properties at the average temperature) (b) exact analysis

Amixture of slurry and mud is to be pumped through a horizontal pipe of diameter 500 mm. the fluid behaves as a bingham plastic with a yield stress of 30 pa and viscosity 0.04 pa.s. describe the effects of the shear stress through a transverse section of the pipe by plotting the variation in shear stress and velocity profile: (i) just before the slurry starts to move (ii) as the slurry flows when the pressure gradient is double that in part (i)