Pressure transmission in Bingham fluids compressed within a closed pipe

This study presents a mathematical model to simulate the pressure transmission that takes place when a Bingham fluid is pressurized at one pipe end and the other is maintained closed. The fluid motion inside the pipe is assumed to be one-dimensional, isothermal, weakly compressible and laminar. The model is based on the continuity and momentum equations which are iteratively solved by the method of characteristics. In contrast with Newtonian fluids, the results point out that Bingham fluids cannot transmit pressure because of the yield stress. In other words, as soon as the pressure gradient along the pipe is not enough to overcome the yield stress the fluid stops moving. A sensitivity analysis also shows that the final pressure gradient along the pipe depends not only on the Bingham number, i.e. yield stress, but also on the relationship between the pipe aspect ratio, the Reynolds and Mach numbers.

► Bingham fluids do not transmit pressure in closed pipes as Newtonian fluids do.
► The final pressure distribution of Bingham fluids in a closed pipe is not uniform.
► The steady-state pressure distribution depends on the pipe aspect ratio and on the Bingham, Reynolds and Mach numbers.