How to Calculate and Solve for Viscosity of Bingham Fluids | Rheology

The image above represents viscosity of bingham fluids.

To compute for viscosity of bingham fluids, three essential parameters are needed and these parameters are Yield Stress (ζy), Shear Rate (γ) and Co-efficient of Rigidity (ηB).

The formula for calculating viscosity of bingham fluids:

ηa = ηB + ζy / γ

Where:

ηa = Viscosity of Bingham Fluids
ζy = Yield Stress
γ = Shear Rate
ηB = Co-efficient of Rigidity

Let’s solve an example;
Find the viscosity of bingham fluids when the yield stress is 21, the shear rate is 18 and co-efficient of rigidity is 14.

This implies that;

ζy = Yield Stress = 21
γ = Shear Rate = 18
ηB = Co-efficient of Rigidity = 14

ηa = ηB + ζy / γ
ηa = 14 + 21 / 18
ηa = 14 + 1.166
ηa = 15.16

Therefore, the viscosity of bingham fluids is 15.16.

Calculating for Yield Stress when the Viscosity of Bingham Fluids, the Shear Rate and the Co-efficient of Rigidity is Given.

ζy = (ηa – ηB) γ

Where;

ζy = Yield Stress
ηa = Viscosity of Bingham Fluids
γ = Shear Rate
ηB = Co-efficient of Rigidity

Let’s solve an example;
Find the yield stress when the viscosity of bingham fluids is 12, the shear rate is 14 and the co-efficient of rigidity is 8.

This implies that;

ηa = Viscosity of Bingham Fluids = 12
γ = Shear Rate = 14
ηB = Co-efficient of Rigidity = 8

ζy = (ηa – ηB) γ
ζy = (12 – 8) 14
ζy = (4) 14
ζy = 56

Therefore, the yield stress is 56.

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