Exact Solution of Tank Drainage for Bingham Fluid flow circular tube

Unsteady tank drainage of Bingham Plastic fluid whose flow of the fluid is due to gravity, is considered in this study. The separation of variables method is used to obtain the exact solution of the fluid. Due to very high yield stress of the fluid no slip condition is used to find out the velocity profile of the fluid. The primary objective of this work is to find the velocity profile, flow rate, shear stress, average velocity, time efflux, the relationship between the time (varying with the depth of a tank) and the time required for complete drainage from emerging partial differential equation. It has been observed that when the Bingham model parameters, flow region and pipe length increase, the time required to drain the fluid from the tank also increases. Furthermore, findings indicate that higher density and a larger pipe radius result in quicker drainage of Bingham plastic fluid from the circular tank.