The viscosity of a fluid depends on the following factors except the?

Analyze the question: We need the factor that does NOT affect a fluid's viscosity.

Concept: Viscosity is the internal friction of a fluid, which is its resistance to the relative motion of its layers. Newton's law of viscosity gives:

F = ηA(dv/dx)

where

• F = viscous force
• η = coefficient of viscosity
• A = area of the layers in contact
• dv/dx = velocity gradient (relative motion between layers)

Going through the options:

• A. Relative motion between the layers: The viscous force exists because adjacent layers move relative to each other, and it depends on the velocity gradient. This is a factor.
• B. Nature of the material of the fluid: η is a property of the fluid itself (honey is far more viscous than water), and it also changes with temperature. This is a factor.
• C. Surface area of the fluid in contact: In F = ηA(dv/dx), the viscous force is proportional to the contact area between the layers. Textbook treatments of this WASSCE question list it as a factor, so it counts as a dependence.
• D. Normal reaction in the fluid: Viscosity arises from molecular interactions between layers moving relative to each other. It does not depend on a "normal reaction". That idea belongs to solid friction, where friction = μR. This is not a factor.

Tip: Do not confuse viscosity with solid friction. Solid friction depends on the normal reaction (F = μR) and is independent of area. Viscous force depends on area, velocity gradient and the nature of the fluid, and has nothing to do with normal reaction.