Fluid Mechanics Chapter 2

- Fundamental Concepts

Fluid as a Continuum

- The region of space in which a fluid properties

such as density could be treated as continuous is

called continuum. - In a continuum each fluid property is expected to

have a definite value at every point in space - So fluid properties of density, temperature and

velocity and so on are considered continuous

function of time in a continuum

Some basics

- So in a continuum, density of a fluid will be
- Specific gravity is a measure of how dense a

fluid is with reference to water - So Mercury is 13.6 times denser than water with a

specific gravity of 13.0 - Specific gravity decreases with increase in TEMP

Some basics

- Specific weight of a substance is weight per unit

volume

Velocity Field

- A very important property defined by a field is

the velocity field, given by - Velocity is a vector quantity, requiring a

magnitude and direction for a complete

description, so the velocity field is a vector

field. - velocity vector, also can be written in terms of

its three scalar components - Velocity field means it is the velocity of a

fluid passing through a point in space with

coordinates X,Y,Z at time instant t. - U,V,W are the components of velocity in X , Y and

Z directions

Basics

- Steady Flow If properties at any point in a

fluid flow donot change with time, it is called a

steady flow. Mathematically for any property - So it could be

Steady Flow

- In a steady flow the fluid properties may vary

from point to point in the field but would remain

constant at that point with respect to time

One-, Two-, and Three-Dimensional Flows

- A flow is classified as one-, two-, or

three-dimensional depending on the number of

space coordinates required to specify the

velocity field - velocity field may be a function of three space

coordinates and time. - Such a flow field is termed three-dimensional

Uniform Flow

- A Flow in which Velocity is constant at any cross

section of flow is called a uniform flow - Under this assumption a 2 dimensional flow is

modeled as one dimensional for analysis. - The density and pressure may also be assumed

constant in the cross section of a uniform flow

Uniform flow field

- A flow field in which velocity is constant and

independent of all space coordinates in the

entire flow field

Timelines , pathlines, streaklines and streamlines

- Pathline It is the path or trajectory of a

moving fluid particle. To identify this a dye

/colour may be added to the fluid and photographs

taken for the particle throughout its motion. - Streakline If we focus our attention on a fixed

location. And identify All the particles which

passed through this location at different draw a

line joining all these particles, the line so

drawn will be called streakline - StreamlinesLines drawn in a flow field so that

at a given instant they are tangent to the flow

direction are called streamlines - Timelines A line marked in a flow and

visualising it how it changes over a period of

time

Timelines , pathlines, streaklines and streamlines

Conclusions

- Steady Flow Streamlines, streaklines and path

lines are the same(identical). - Unsteady flow All these lines are different

Mathematically deriving streamlines and pathlines

- Streamlines
- Pathline A simulataneous solution of following

equations give path line in

Mathematically deriving streamlines and pathlines

- Streaklines First derive the path lines and the

apply following formulas

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End of Part I of the Chapter