BASIC CONCEPTS

• •  Mechanics is the oldest physical science that deals with both stationery and moving boundaries under the influence of forces. The branch of the mechanics that deals with bodies at rest is called statics while the branch that deals with bodies in motion is called dynamics.

•  Fluid Mechanics is the science that deals with behavior of fluids at rest (fluid statics) or in motion (fluid dynamics) and the interaction of fluids with solids or other fluids at the boundaries.

•  A substance in liquid / gas phase is referred as ‘fluid'. Distinction between a solid & a fluid is made on the basis of substance's ability to resist an applied shear (tangential) stress that tends to change its shape. A solid can resist an applied shear by deforming its shape whereas a fluid deforms continuously under the influence of shear stress, no matter how small is its shape. In solids, stress is proportional to strain, but in fluids, stress is proportional to ‘strain rate.'

Fig. 1.1.1: Illustration of solid and fluid deformation.

• Referring to Fig. 1.1.1, the shear modulus of solid (S) and coefficient of viscosity (μ) for fluid can defined in the following manner;

 

(1.1.1)

• Here, the shear force (F) is acting on the certain cross-sectional area (A), h is the height of the solid block / height between two adjacent layer of the fluid element, Δx is the elongation of the solid block and Δu is the velocity gradient between two adjacent layers of the fluid.

•  Although liquids and gases share some common characteristics, they have many distinctive characteristics on their own. It is easy to compress a gas whereas liquids are incompressible. A given mass of the liquid occupies a fixed volume, irrespective of the size and shape of the container. A gas has no fixed volume and will expand continuously unless restrained by the containing vessel. For liquids a free surface is formed in the volume of the container is greater than that of the liquid. A gas will completely fill any vessel in which it is placed and therefore, does not have a free surface.

Dimension and Unit

A dimension is the measure by which a physical variable is expressed quantitatively and the unit is a particular way of attaching a number to the quantities of dimension. All the properties of fluid are assigned with certain unit and dimension. Some basic dimensions such as mass (M), length (L), time (T) and temperature ( q ) are selected as Primary/Fundamental dimensions/unit. While others such as velocity, volume is expressed in terms of primary dimensions and is called as secondary/derived dimensions/unit. In this particular course, SI (Standard International) system of units and dimension will be followed to express the properties of fluid.

Fluid as Continuum

Fluids are aggregations of molecules; widely spaced for a gas and closely spaced for liquids. Distance between the molecules is very large compared to the molecular diameter. The number of molecules involved is immense and the separation between them is normally negligible. Under these conditions, fluid can be treated as continuum and the properties at any point can be treated as bulk behavior of the fluids .

For the continuum model to be valid, the smallest sample of matter of practical interest must contain a large number of molecules so that meaningful averages can be calculated. In the case of air at sea-level conditions, a volume of 10^-9 mm³ contains 3×10⁷ molecules. In engineering sense, this volume is quite small, so the continuum hypothesis is valid.

In certain cases, such as, very-high-altitude flight, the molecular spacing becomes so large that a small volume contains only few molecules and the continuum model fails. For all situations in these lectures, the continuum model will be valid.