# Bingham Number

on . Posted in Dimensionless Numbers

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.

### Key Points about Bingham number

• If Bm is much greater than 1  -  The yield stress dominates, and the fluid behaves like a solid until enough force is applied to overcome the yield stress.
• If Bm is much less than 1  -  The fluid behaves as a regular Newtonian fluid, where the shear stress is directly proportional to the velocity gradient.

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.

### Bingham Number formula

$$Bm = \tau_y \; l_c \;/\; \mu\; v$$     (Bingham Number)

$$\tau_y = Bm \; \mu\; v \;/\; l_c$$

$$l_c = Bm \; \mu\; v \;/\; \tau_y$$

$$\mu\ = \tau_y \; l_c \;/\; Bm \; v$$

$$v = \tau_y \; l_c \;/\; Bm \; \mu$$

### Solve for Bm

 yield stress, τy characteristic length, lc dynamic viscosity, μ velocity, v

### Solve for τy

 Bingham number, Bm dynamic viscosity, μ velocity, v characteristic length, lc

### Solve for lc

 Bingham number, Bm dynamic viscosity, μ velocity, v yield stress, τy

### Solve for μ

 yield stress, τy characteristic length, lc Bingham number, Bm velocity, v

### Solve for v

 yield stress, τy characteristic length, lc Bingham number, Bm dynamic viscosity, μ

Symbol English Metric
$$Bm$$ = Bingham number $$dimensionless$$
$$\tau_y$$  (Greek symbol tau) = yield stress $$lbf \;/\;in^2$$ $$Pa$$
$$l_c$$ = characteristic length $$ft$$ $$m$$
$$\mu$$  (Greek symbol mu) = dynamic viscosity of fluid $$lbf-sec \;/\; ft^2$$ $$Pa-s$$
$$v$$ = velocity $$ft \;/\; sec$$ $$m \;/\; s$$

Tags: Pipe Flow