Q6/ Bingham plastic in a vertical tube,. A long vertical pipe of radius a and length L, open to the atmosphere at both ends, is filled with a Bingham plastic of density p and rheological parameters 70 and no. If the z axis points vertically downwards, prove that the shear-stress distribution is given by: Trz τρα 2 Derive an expression for the minimum pipe radius, amin, that will just cause flow of the Bingham plastic under gravity. Your answer should be in terms of any or all of the parameters: p, to, no, L, and, You may assume that: g. 1/17 |მ. :T= * = Ər If a pipe of radius 2amin is now filled with the same material, and both ends are allowed to communicate with the atmosphere, derive the velocity profile vz as a function of r and any or all of the parameters previously listed.