## Bingham Number

Bingham Number Calculator

## Bingham Number Calculator

The Bingham number (Bn) is a dimensionless parameter used in fluid mechanics to characterize the relative importance of viscous forces to gravitational forces in a fluid flow situation. It’s named after after Eugene C. Bingham, an American chemist and rheologist who made significant contributions to the study of viscoplastic fluids.

Bingham number is proportional to { (yield stress) / (viscous stress) } and is used in momentum transfer in general and flow of bingham plastics calculations in particular. It is normally defined in the following form :

 Where: gc = Dimensional constant L = Characteristic length mu = Viscosity 𝜏y = Stress V = Velocity

The Bingham number helps determine whether a fluid behaves as a solid (with a yield stress that must be exceeded for flow to occur) or as a fluid (where flow occurs even without applied shear stress).

Depending on the value of the Bingham number, different flow regimes can be identified:

• If Bn << 1, viscous forces dominate, and the fluid behaves as a Newtonian fluid, where flow occurs continuously even at low shear stress levels.
• If Bn >> 1, gravitational forces dominate, and the fluid behaves as a Bingham plastic, where flow only occurs when the applied shear stress exceeds the yield stress.

The Bingham number is commonly used in the analysis of viscoplastic fluids, such as mud flows in drilling operations, toothpaste squeezing, and certain types of food processing. It helps engineers and scientists understand and predict the flow behavior of these materials under different conditions.

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