Module 2-Lecture Slide 1

ME 203 Mechanics of Fluids

Module-II

Fluid Kinematics

• Fluid kinematics deals with describing the motion of fluids without necessarily considering the forces and moments that cause the motion .

• It is generally a continuous function in space and time.

• A fluid motion is typically described by velocity field defined as,

• There are two frames of reference for describing this motion

Lagrangian

“moving reference frame”

Eulerian

Lagrangian Description

Lagrangian Description

Lagrangian Description

Eulerian Description

• In the Eulerian description of fluid flow, individual fluid particles are not identified. Instead, a control volume is defined.

• Each property is expressed as a function of space and time

Eulerian Description

Types of Flow

 Ideal and Real flow.

 Compressible and Incompressible flow.

 Depending upon properties of flow

 Laminar and turbulent flow.

 Steady and unsteady flow.

 Uniform and Non-uniform flow.

 Rotational and Irrotational flow.

 One, two and three dimensional flow.

Types of fluid Flow

Real and Ideal Flow:

Friction = 0

Ideal Flow ( μ =0) Energy loss =0

Friction = o

Real Flow ( μ ≠0) Energy loss = 0

Ideal _Real

If the fluid is considered frictionless with zero viscosity it is called ideal.

In real fluids the viscosity is considered and shear stresses occur causing

Compressible and Incompressible

flows

 Incompressible fluid flows assumes the fluid have constant

Laminar and turbulent flow

The flow in which adjacent layer do not cross to each other and move along the well define path is called as

laminar flow.

Laminar flow

Turbulent flow

Transition of flow from Laminar to turbulent

• Laminar Flow

Layers of water flow over one another at different speeds with virtually no mixing between layers.

• Turbulent Flow

The flow is characterized by the irregular movement of particles of the fluid.

Reynold’s experiment

Reynold’s experiments involved injecting a dye streak into fluid moving at constant velocity through a transparent tube.

Dye followed a straight path.

Dye followed a wavy path with streak intact.

Dye rapidly mixed through the fluid in the tube

Reynolds classified the flow type according to the motion of the fluid.

Laminar Flow: every fluid molecule followed a straight path that was parallel to the

boundaries of the tube.

Turbulent Flow: every fluid molecule followed very complex path that led to a mixing of the dye.

Transitional Flow: every fluid molecule

Reynolds found that conditions for each of the flow types depended on:

1. The velocity of the flow (U) 2. The diameter of the tube (D)

3. The density of the fluid (r). 4. The fluid’s dynamic viscosity (m).

He combined these variables into a dimensionless combination now known as the Flow Reynolds’ Number (R) where:

UD

r

m



UD

r

m



R

Flow Reynolds’ number is often expressed in terms of the fluid’s kinematic viscosity (n; lower case Greek letter nu), where:

m

n

r



UD

n



R

r

m



Substituting into R:

r

r

UD



Steady and Unsteady Flow

H=constant

V=constant

Steady Flow with respect to time

•Velocity is constant at certain position w.r.t. time

Unsteady Flow with respect to time •Velocity changes at certain position w.r.t. time

H ≠ constant

V ≠ constant

Steady flow occurs when conditions of a point in a flow field don’t change with respect to time ( v, p, H…..changes w.r.t. time

 

 

 

 

Uniform Flow means that the velocity is constant at certain time in different positions (doesn’t depend on any dimension x or y or z(

Non- uniform Flow means velocity changes at certain time in different positions ( depends on dimension

Rotational & Irrotational Flow

 Rotational Flows

:-

 The flow in which fuid particle while flowing along stream lines rotate about their own axis is called as rotational flow.

 Irrotational Flows:-

One, Two and Three Dimensional

Flows

 Although in general all fluids flow three-dimensionally, with pressures and velocities and other flow properties varying in all directions, in many cases the greatest changes only occur in two directions or even only in one. In these cases changes in the other direction can be effectively ignored making analysis much more simple.

One, Two and Three Dimensional

Flows

 Flow is two-dimensional : if it can be assumed that the flow parameters vary in the direction of flow and in

one direction at right angles to this direction.

Visualization of flow Pattern

• Most fluids (air, water, etc.) are transparent, thus their flow patterns are invisible to us. Flow visualization is used to make flow patterns visible so that we can visually acquire qualitative and quantitative flow information.

• To understand the fluid flow effectively we have to visualize it graphically. Pathlines, Streaklines and Streamlines provide a vivid visualization of a fluid flow.

Visualization of flow Pattern

in time and space, but in order to visualize the flow pattern it is useful to define some other properties of the flow. These definitions correspond to various experimental methods of visualizing fluid flow. They are :

a. Streamlines b. Pathlines c. Streak lines

Streamlines

• Streamlines are the Geometrical representation of the of the flow velocity.

Streamlines

• In an unsteady flow where the velocity vector changes with time, the pattern of streamlines also changes from instant to instant.

•

• In a steady flow, the orientation or the pattern of streamlines will be fixed.

• There can be no flow across the streamlines as they are tangent to the velocity at every point in the flow.

Streamlines

Pathlines

Streakline

 A streakline is the locus of fluid particles that have passed sequentially through a prescribed point in the flow.

Timelines

Material and Local Derivatives

• In Lagrangian approach, a material of the fluid is identified, tracked (or followed) it as it moves, and monitored the change in its properties. The properties may be velocity, temperature, density, mass, or concentration, etc in the flow field. The time change of the temperature in such a measurement is denoted as which called material derivative or substantial derivative. Thus the material derivative is a Lagrangian derivative and is denoted as

• Thus the Lagrangian derivative contains an extra term besides the Eulerian derivative. The first term on the right hand side is called the