In an article, the maximum shear stress τ of a cracked concrete member is given to be τ = τ0(1 − kw), where τ0 is the maximum shear stress for a crack width of zero, w is the crack width in mm, and k is a constant estimated from experimental data. Assume k = 0.28 ± 0.04 mm−1. Given that τ0 = 50 MPa and w = 1.0 mm, both with negligible uncertainty, estimate τ and find the uncertainty in the estimate.

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)