Three alloys were found to have the hall-petch parameters shown in the following table. alloy σ0 (mpa) ky (mpa mm1/2) a 90 9.2 b 75 6.1 c 170 2.3 which alloy has the highest yield strength for a grain size of 20 microns? which alloy will benefit the most from grain refinement? explain your answer.

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)