For a Newtonian Fluid:

CONCEPT:

Newton's law of Viscous Force:

• According to Newton's hypothesis, the tangential force ‘F’ acting on a plane parallel layer is proportional to the area of the plane ‘A’ and the velocity gradient \(\frac{{dv}}{{dx}}\) in a direction normal to the layer,

\(F = - \eta A\frac{{dv}}{{dx}}\)

Where η = coefficient of viscosity, A = area of the plane, and dv/dx = velocity gradient.

• A negative sign is employed because viscous force acts in a direction opposite to the flow of liquid.
• The SI unit of viscosity is poiseiulle (Pl). Its other units are Nsm-2 or Pa s.

EXPLANATION:

• Newtonian fluids defined as fluids for which the shear stress is linearly proportional to the shear strain rate. Therefore the shear stress-strain graph for a Newtonian fluid is a straight line. Hence, option 1 is correct. The fluids, such as air, kerosene, gasoline, and other oil-based liquids, are Newtonian fluids.
• Newtonian fluids are analogous to elastic solids (Hooke’s law: stress proportional to strain).
• Fluids for which the shear stress is not linearly related to the shear strain rate are called non- Newtonian fluids. Examples include slurries, colloidal suspensions, polymer solutions, blood, paste, and cake batter.