1. 1. Integral vs Differential Approach
Fluid flows may be analysed using -
Integral Approach
will not give a point by point
description of Fluid Motion.
Gives only the overall
effect of fluid motion
on a structure or body
Differential Approach
Does give a point by point
description of Fluid Motion or

2. 2. Lagrangian vs Eulerian Methods
Lagrangian Method
A system approach to track of
a fixed mass of fluid.
Complicated
Eulerian Method
Studies what happens at a point
or within a Control Volume
Convenient y
(x0,y0,t) a b
Pa = Pa(t)
Pb = Pb(t)
Pc = Pc(t) x c
P=P(x,y,t)

3. 3. System and Control Volume
System is a fixed mass of fluid,
its boundaries may change with
time.
A Control Volume is a region
in space, mass can cross its
boundary

4. 4. Conditions on Fluid Motion
Systems are subject to
Law of Conservation of Mass :
Newton’s Second Law of Motion:
First and Second Laws of Thermodynamics:
To calculate a flow we need in addition
Equation of State
A formula/Equation for Viscosity
Boundary Conditions

5. 5. Reynolds Transport Theorem

6. 6. Continuity Equation (N = m, h = 1)v2 v1
dA2
dA1 2 1
Steady Flow-
Which for a stream tube becomes
Incompressible flow:
For an incompressible flow

7. 7. Momentum Equations (N=mV and h = v)
Fs Surface force
Fb Body force
d Volume element
dA Area element

8. 8. Energy Equation For a steady incompressible flow one has
E, Total Energy,
Internal Energy, g acceleration due to gravity, ,
Z elevation,
Qentry
Rate of Heat Addition,
Wentry Work done on the system.
For a steady incompressible flow one has