1. FLUID DYNAMICS

2. Content Uniform Flow, Steady Flow Flow rate. Continuity
The Bernoulli Equation - Work and Energy
Applications of the Bernoulli Equation
The Momentum Equation
Application of the Momentum Equation

11. INTRODUCTION
Fluid dynamics is the study of the movement of fluids, including their interactions as two fluids come into contact with each other
It is not difficult to envisage a very complex fluid flow. Spray behind a car; waves on beaches; hurricanes and tornadoes or any other atmospheric phenomenon are all example of highly complex fluid flows which can be analysed with varying degrees of success

12. WAYS TO DESCRIBE FLUID MOTION
There are two ways of describing the motion of a fluid:
LAGRANGIAN AND EULERIAN DESCRIPTIONS

13. LAGRANGIAN DESCRIPTION
Named after the Italian mathematician Joseph Louis Lagrange (1736–1813
The Lagrangian description requires us to track the position and velocity of each individual fluid parcel, which we refer to as a fluid particle, and take to be a parcel of fixed identity
Can we do same for fluids?

14. First of all we cannot easily define and identify fluid particles as they move around.
Secondly, a fluid is a continuum (from a macroscopic point of view), so interactions between fluid particles are not as easy to describe as are interactions between distinct objects like billiard ball
Furthermore, the fluid particles continually deform as they Move in the flow
From a microscopic point of view, a fluid is composed of billions of molecules that are continuously banging into one another,

15. APPLICATION
There are many practical applications of the Lagrangian description,
tracking of passive scalars in a flow to model contaminant transport,
rarefied gas dynamics calculations concerning reentry of a spaceship into the earth’s atmosphere
development of flow visualization and measurement systems based on particle tracking

16. EULERIAN DESCRIPTIONS
named after the Swiss mathematician Leonhard Euler (1707–1783)
A finite volume called a flow domain or control volume is defined, through which fluid flows in and out. Instead of tracking individual fluid particles, we define field variables, functions of space and time, within the control volume

17. These (and other) field variables define the flow field.

18. Lagarangian Vs Eulerian method
Measurement of temperature

19. Velocity field- Uniform Vs Non-Uniform

20. Uniform flow and Non-uniform flow
Uniform flow Flow is said to be uniform, when the velocity of flow does not change either in magnitude or in direction at any point in a flowing fluid, for a given time. For example, the flow of liquids under pressure through long pipelines with a constant diameter is called uniform flow.
Non-uniform flow Flow is said to be non-uniform, when there is a change in velocity of the flow at different points in a flowing fluid, for a given time. For example, the flow of liquids under pressure through long pipelines of varying diameter is referred to as non-uniform flow. All these type of flows can exist independently of each other

21. Velocity field- Steady Vs Unsteady

22. Steady flow and Unsteady flow
Steady flow Fluid flow is said to be steady if at any point in the flowing fluid, important characteristics such as pressure, density, velocity, temperature, etc. that are used to describe the behavior of a fluid, do not change with time. In other words, the rate of flow through any crosssection of a pipe in a steady flow is constant.
Unsteady flow Fluid flow is said to be unsteady if at any point in the flowing fluid any one or all the characteristics describing the behavior of a fluid such as pressure, density, velocity and temperature change with time. Unsteady flow is that type of flow, in which the fluid characteristics change with respect to time or in other words, the rate of flow through any cross-section of a pipe is not constant

23. Steady non-uniform flow, Unsteady uniform flow and Unsteady non-uniform flow
Steady non-uniform flow. Conditions change from point to point in the stream but do not change with time. An example is flow in a tapering pipe with constant velocity at the inlet - velocity will change as you move along the length of the pipe toward the exit.
Unsteady uniform flow. At a given instant in time the conditions at every point are the same, but will change with time. An example is a pipe of constant diameter connected to a pump pumping at a constant rate which is then switched off.
Unsteady non-uniform flow. Every condition of the flow may change from point to point and with time at every point. For example waves in a channel

24. 3 DIMENSIONAL FLOW
Term one, two or three dimensional flow refers to the number of space coordinated required to describe a flow.
Most fluid flows are complex three dimensional, time-dependent phenomenon, however we can make simplifying assumptions allowing an easier analysis or understanding without sacrificing accuracy. In many cases we can treat the flow as 1D or 2D flow.
In these cases changes in the other direction can be effectively ignored making analysis much more simple

25. 1 DIMENSIONAL FLOW
if the flow parameters (such as velocity, pressure, depth etc.) at a given instant in time only vary in the direction of flow and not across the cross-section.
In reality flow is never one dimensional because viscosity causes the velocity to decrease up to zero at boundaries.
An example of one-dimensional flow is the flow in a pipe

26. 1 DIMENSIONAL FLOW
A characteristic of this flow is that the velocity becomes invariant in the flow direction as shown in the figure
It is seen that velocity at any location depends just on the radial distance  from the centreline and is independent of distance, x or of the angular position . This represents a typical one-dimensional flow

27. 2 DIMENSIONAL FLOW
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.
In many situations one of the velocity components may be small relative to the other two, thus it is reasonable in this case to assume 2D flow
Streamlines in two-dimensional flow are curved lines on a plane and are the same on all parallel planes. .

28. Now consider a flow through a diverging duct as shown next
Now consider a flow through a diverging duct as shown next. Velocity at any location depends not only upon the radial distance  but also on the x-distance. This is therefore a two-dimensional flow

29. 3 DIMENSIONAL FLOW
All three velocity components are important and of equal magnitude. Flow past a wing is complex 3D flow, and simplifying by eliminating any of the three velocities would lead to severe errors

30. Flow Visualization
Flow visualization is the visual examination of flow-field features.
Important for both physical experiments and numerical (CFD) solutions.
Numerous methods
Streamlines and streamtubes
Pathlines
Streaklines
Timelines
Refractive techniques
Surface flow technique

31. Streamlines and streamtubes

32. surface pressure contours and streamlines

33. Pathlines

34. Streakline

35. ASSIGNMENT
A weather balloon is launched into the atmosphere by meteorologists. When the balloon reaches an altitude where it is neutrally buoyant, it transmits information about weather conditions to monitoring stations on the ground. Is this a Lagrangian or an Eulerian measurement? Explain.

36. ASSIGNMENT
A steady, incompressible, two-dimensional velocity field is given by
where the x- and y-coordinates are in meters and the magnitude of velocity is in m/s. A stagnation point is defined as a point in the flow field where the velocity
is zero. (a) Determine if there are any stagnation points in this flow field and, if so, where?

37. Flow rate.