Bingham Number Of Plastic Fluids From Isothermal Semi-Circular Cylinder Calculator

Bingham Number Formula:

\[ Bn = \frac{\zeta_o}{\mu_B} \times \left( \frac{D_1}{g \times \beta \times \Delta T} \right)^{0.5} \]

Fluid Yield Stress (ζo):

Plastic Viscosity (μB):

Pa·s

Diameter of Cylinder 1 (D1):

Acceleration due to Gravity (g):

m/s²

Coefficient of Volumetric Expansion (β):

K⁻¹

Change in Temperature (ΔT):

Bingham Number (Bn):

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1. What is the Bingham Number?

The Bingham Number is a dimensionless quantity used in fluid mechanics to characterize the flow of Bingham plastic fluids. It represents the ratio of yield stress to viscous stress and helps determine whether a fluid will flow under given conditions.

2. How Does the Calculator Work?

The calculator uses the Bingham Number formula:

\[ Bn = \frac{\zeta_o}{\mu_B} \times \left( \frac{D_1}{g \times \beta \times \Delta T} \right)^{0.5} \]

Where:

\( \zeta_o \) — Fluid Yield Stress (Pa)
\( \mu_B \) — Plastic Viscosity (Pa·s)
\( D_1 \) — Diameter of Cylinder 1 (m)
\( g \) — Acceleration due to Gravity (m/s²)
\( \beta \) — Coefficient of Volumetric Expansion (K⁻¹)
\( \Delta T \) — Change in Temperature (K)

Explanation: The equation calculates the dimensionless Bingham Number by considering the fluid properties, geometric parameters, and thermal conditions.

3. Importance of Bingham Number Calculation

Details: The Bingham Number is crucial for understanding the flow behavior of non-Newtonian fluids, particularly Bingham plastics. It helps in designing industrial processes, predicting flow patterns, and optimizing fluid transport systems.

4. Using the Calculator

Tips: Enter all required parameters in appropriate units. Ensure all values are positive and within reasonable physical limits for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What are Bingham plastic fluids?
A: Bingham plastics are non-Newtonian fluids that require a minimum yield stress to start flowing but behave like Newtonian fluids once flow begins.

Q2: What is a typical range for Bingham Numbers?
A: Bingham Numbers can vary widely depending on the fluid and conditions, ranging from very small values for near-Newtonian fluids to large values for highly yield-stress fluids.

Q3: How does temperature affect the Bingham Number?
A: Temperature affects both yield stress and viscosity, which in turn influence the Bingham Number. The temperature change parameter accounts for thermal effects on fluid properties.

Q4: What industries use Bingham Number calculations?
A: This calculation is important in petroleum, chemical, food processing, and construction industries where non-Newtonian fluids are common.

Q5: Are there limitations to this equation?
A: The equation assumes isothermal conditions for semi-circular cylinders and may need modifications for complex geometries or non-isothermal conditions.