Bingham Fluid Flow in a Circular Tube

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

A Bingham fluid acts like a rigid body at low shear stress but flows like a viscous fluid at high shear.


Consider the laminar flow of a Bingham fluid in a long circular tube of radius and length . The fluid flows under the influence of a pressure difference . The fluid density is .

One can derive an analytical expression for the velocity, given by

for ,

for ,

where .

The mass flow rate is given by:

, with .

Here is the zero–shear viscosity and is the yield stress. You can vary these two parameters.

For a Newtonian fluid, the mass flow rate is given by the Hagen–Poiseuille equation: .

This Demonstration plots the velocity profile (blue curve) and gives the value of the corresponding mass flow rate. In addition, the velocity profile for a Newtonian fluid is plotted (red curve). The viscosity, , of the Newtonian fluid is chosen such that both fluid mass flow rates are equal. The value of the viscosity, , is also shown.


Contributed by: Housam Binous (December 2010)
Open content licensed under CC BY-NC-SA


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.