Question

1- What is the continuum assumption? Why do we make this assumption in fluid mechanics?

2-Describe Newtonian and non- Newtonian fluids and give examples?

3-Define Mach number, and describe compressible and incompressible flows?

Answer 1

Answer 1: Continuum is an assumption that is made in subjects in order to simplify the practical situation. We know that there are atoms that are continuously collided with each other within the fluid at a microscopic level. There must be some micro volumes where there are no particles present at the moment because of turbulence at micro level. But in practical, we simply assume that the fluid is continuous over the volume under the consideration without any voids present. If we say fluid has a density of 1000 kg/m³ , then we have already taken the continuum assumption and for unit volume fluid has a mass of 1000 kg.

Without Continuum assumption, practical situations become too complex and their understanding would be difficult.

Answer 2: Newtonian Fluid:  These are considered as the ideal fluids. There is a relation between Shear stress applied over the fluid and the shear strain produced. This relation is called as Newton's law of viscousity.   

Newtonian fluids follow this relation. There is a linear relation between the magnitude of shear stress and the resulting rate of deformation and the constant of proportionality also does not change with deformation. Examples :Water, organic solvents, Single grade motor oil.

Non Newtonian Fluids: In these fluids,there is a non linear relationship between the magnitude of applies stressand the rate of angular deformation. Examples : paint, colloidal solution, toothpaste.

Answer 3: Mach Number :Mach number at a point in a flow can be written as the ratio of velocity of fluid to velocity of sound( sonic velocity) in the same fluid medium corresponding to the values of bulk modulus and density existing at the point where the velocity is measured.

Compressible fluids :Compressible fluids are those in which density variation is appreciable under pressure. In th analysis of compressible fluids, a factor called compressibily plays a signnificant role.

Incompressible fluids : Those fluids for which density does not changes when pressure is applied.