What type of fluid has a linear shear stress?

What type of fluid has a linear shear stress?

• A. Newtonian Fluid
• B. Pseudoplastic
• C. Dilatant
• D. Bingham Plastic

Answer: (D)

A Bingham Plastic shows linear stress growth once it starts to flow. It behaves like a solid until the applied shear stress exceeds a yield stress, and beyond that point the relationship between shear stress and shear rate is linear: tau = tau_y + mu_p * gamma_dot. The slope mu_p is the plastic viscosity, and the intercept tau_y is the yield stress. This creates a straight-line relationship in the flowing regime, which is what the statement about linear shear stress refers to. Other fluids either have a linear relationship through the origin (Newtonian) or exhibit nonlinear changes in viscosity with shear rate (pseudoplastic and dilatant), so they don’t match the described behavior.

A Bingham Plastic shows linear stress growth once it starts to flow. It behaves like a solid until the applied shear stress exceeds a yield stress, and beyond that point the relationship between shear stress and shear rate is linear: tau = tau_y + mu_p * gamma_dot. The slope mu_p is the plastic viscosity, and the intercept tau_y is the yield stress. This creates a straight-line relationship in the flowing regime, which is what the statement about linear shear stress refers to. Other fluids either have a linear relationship through the origin (Newtonian) or exhibit nonlinear changes in viscosity with shear rate (pseudoplastic and dilatant), so they don’t match the described behavior.