Consider the following statements related to the coefficient of dynamic viscosity \((\mu)\) and temperature (T) and choose the incorrect options).
a. For water, '\(\mu\)' decreases when '\(T\)' increases
b. For water, '\(\mu\)' increases when '\(T\)' increases
c. For water, '\(\mu\)' decreases when '\(T\)' increases
d. For Air, '\(\mu\)' decreases when '\(T\)' increases

Explanation:

• Dynamic viscosity of water decreases with increase in temperature.

• As temperature rises, intermolecular forces weaken, making fluid layers slide more easily.

• For gases like air, dynamic viscosity increases with temperature.

• Higher temperature leads to more molecular motion, increasing momentum transfer between layers.

 Additional Information Dynamic Viscosity (μ)

• It measures a fluid’s resistance to flow when an external force is applied.

• Represents internal friction between fluid layers moving at different velocities.

• SI unit: Pascal-second (Pa·s) or N·s/m².

• For liquids, μ decreases as temperature increases.

• For gases, μ increases with temperature.

• Used in calculating shear stress and analyzing force in fluid motion.

Kinematic Viscosity (ν)

• It is the ratio of dynamic viscosity to fluid density.

• Describes how easily a fluid flows under gravity.

• SI unit: m²/s.

• $\nu = \mu / \rho$ — higher ν means more sluggish flow.

• Depends on both viscosity and density of fluid.

• Useful in flow problems where gravity and motion dominate over external forces.