Bingham Number formula |
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\( Bm \;=\; \dfrac{ \tau_y \cdot l_c }{ \mu\cdot v }\) (Bingham Number) \( \tau_y \;=\; \dfrac{ Bm \cdot \mu\cdot v }{ l_c }\) \( l_c \;=\; \dfrac{ Bm \cdot \mu\cdot v }{ \tau_y }\) \( \mu\ \;=\; \dfrac{ \tau_y \cdot l_c }{ Bm \cdot v } \) \( v \;=\; \dfrac{ \tau_y \cdot l_c }{ Bm \cdot \mu }\) |
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| Symbol | English | Metric |
| \( Bm \) = Bingham Number | \(dimensionless\) | \(dimensionless\) |
| \( \tau_y \) (Greek symbol tau) = Yield Stress | \(lbf \;/\;in^2\) | \(Pa\) |
| \( l_c \) = Characteristic Length | \(ft\) | \(m\) |
| \( \mu \) (Greek symbol mu) = Fluid Dynamic Viscosity | \(lbf-sec \;/\; ft^2\) | \( Pa-s \) |
| \( v \) = Velocity | \(ft \;/\; sec\) | \(m \;/\; s\) |
Bingham number, abbreviated as Bm, a dimensionless number, is the ratio of yield stress to visvous stress. In fluid dynamics and rheology to characterize the flow behavior of certain types of fluids known as Bingham fluids. Bingham fluids exhibit a yield stress, which means they require a certain amount of applied force (stress) before they start to flow. Once this yield stress is exceeded, the fluid behaves like a viscous fluid and flows freely. The Bingham number indicates the relative importance of the yield stress compared to the viscous forces in the fluid flow.
Bingham Number Interpretation
- Low Bingham Number (Bm << 1) - The fluid behaves as a regular Newtonian fluid, where the shear stress is directly proportional to the velocity gradient.
- High Bingham Number (Bm >> 1) - The yield stress dominates, and the fluid behaves like a solid until enough force is applied to overcome the yield stress.
Bingham fluids are commonly found in various industrial applications, such as drilling fluids, certain food products, and certain types of paints and coatings. Understanding the Bingham number helps engineers and scientists predict the flow behavior of these fluids and design appropriate processes and equipment.
