1. Fluid kinematics Chapter 3
Description and visualization of fluid’s motion (velocity, acceleration).

2. Fluid Flow
An ideal fluid is a fluid that has no internal friction or viscosity and is incompressible.
The ideal fluid model simplifies fluid-flow analysis
No real fluid has all the properties of an ideal fluid, it helps to explain the properties of real fluids.

11. LAGRANGIAN AND EULARIAN METHODS OF STUDY OF FLUID FLOW
In the Lagrangian method a single particle is followed over the flow field, the co-ordinate system following the particle. The flow description is particle based and not space based. A moving coordinate system has to be used.
In the Eularian method, the description of flow is on fixed coordinate system based and the description of the velocity etc. are with reference to location and time i.e., V = V (x, y, z, t)

12. Principles of Fluid Flow 1/2
The continuity equation results from conservation of mass:
mass in=mass out
ρQ (in)= ρQ (out)
Continuity equation:
A1V1 = A2V2
Area  speed in region 1 = area  speed in region 2
For liquid, same density

13. Principles of Fluid Flow 2/2
The speed of fluid flow depends on cross-sectional area.
Bernoulli’s principle states that the pressure in a fluid decreases as the fluid’s velocity increases.
P1>P2 & V1<V2
A1V1 = A2V2

14. Flow Rate Volume rate of flow Mass flow rate
Constant velocity over cross-section
Variable velocity
Mass flow rate

15. Examples Example. 1 Discharge in a 25cm pipe is 0.03 m3/s. What is the
average velocity?
Example. 2
A pipe whose diameter is
8 cm transports air with
a temp. of 20oC and
pressure of 200 kPa
abs. At 20 m/s, what is
the mass flow rate?

16. Flow Rate
Only x-direction component of velocity (u) contributes to flow through cross-section

17. Example:
Find the ratio
of velocities:

21. Example

23. Example

24. a) b)

25. c)

26. Example Find inlet velocity, if head increases by 0.1cm/s
Continuity equation

27. Example: The open tank in the figure contains water at 20°C.
For incompressible flow,
derive an analytic expression for dh/dt in terms of (Q1, Q2, Q3).
(b) If h is constant, determine V2 for
the given data if:
V1 = 3 m/s and Q3 = 0.01 m3/s.
Volume=Atank.h =0

28. The Energy Balance (First Law of Thermodynamics)

29. Conservation of energy - 1st law of thermodynamics
“when heat or work are transferred to a control mass this will result in change of energy stored in it”
Q heat added to the system
W work done by the system

30. The Energy Balance Reminder: The general balance equation is: -
Rate of Rate of Rate of Rate of Rate of
Creation – Destruction + Flow in – Flow out = Accumulation
In nature energy can be neither created nor destroyed. With respect to a control volume (CV):
Rate of energy flow into CV
Rate of energy efflux from CV
Rate of accumulation of energy into CV - =
(1)
Units [Energy/time]

31. The Energy Balance Rate of Energy Flow into CV:
Rate of Energy Flow out of CV:
Rate of Energy Accumulation:
e [=J/kg] is the specific energy: e (internal) + e (kinetic)+ e (potential=gravity)
e = u + V2/ 2+ g z

32. Landau Potential (Grand potential)
Name
Symbol
Formula
Natural variables
Internal energy   
                         
                        
Helmholtz free energy
         
Enthalpy
                       
Gibbs free energy
                 
Landau Potential (Grand potential)
where T = temperature, S = entropy, p = pressure, V = volume. The Helmholtz free energy is often denoted by the symbol F, but the use of A is preferred by IUPAC [2]. Ni is the number of particles of type i in the system and μi is the chemical potential for an i-type particle

33. The Energy Balance Substituting in equation (1) :
Q and W are positive when transferred from surroundings to system.
MODERN Convention
Note: 2nd edition of textbook uses old convention: Q is positive when transferred from surroundings to system. W is positive when transferred from system to surroundings

34. The Energy Balance The energy balance reduces to:
(2)
The work term includes:
Shaft work, Wshaft
Work due to pressure (injection work)

35. pressure

36. The Energy Balance The net work is:
Where specific volume u = 1/  [m3/kg]
Jule (j)= N.m
From (2):
(3)
This is the Energy equation

37. The Energy Balance We may use the enthalpy as: h = u + P/ρ
For multiple inlets – outlets the energy equation becomes:
(4)
We may use the enthalpy as: h = u + P/ρ

38. Simplification of Energy Equation
For single inlet (1) – outlet (2) and steady-state conditions
(ie no accumulation of energy and mass) ,
The energy equation becomes:
(5)

39. +