TYPES OF FLUID FLOW CLASS NOTES FOR ENGINEERS
TYPES OF FLUID FLOW CLASS
NOTES FOR ENGINEERS
There are different types of flows
for a moving fluid. The study of
moving fluids is quite complex,
tedious and time consuming. But
the analysis can be made simple by
making one or more simplifying
assumptions e.g., onedimensional
flow, steadystate flow, nonviscous
flow, compressible and incompressible flow.
Compressible flow is that branch of
fluid mechanics which deals with flow
of fluids having significant changes in
fluid density. Gases display such a
behavior since liquids are incompressible.
Mach number (the ratio of the speed of
the fluid flow to the speed of sound)
decides about the compressible and
incompressible flow. When Mach
number is greater than 0.3, it is a
compressible flow since as Mach
number (M) increases, the density
changes become significant. This
flow is found in highspeed aircraft,
spaceexploration vehicles, jet
engines, gas pipelines, modern aircraft,
missiles, and spacecraft. Compressible
fluid flow study is complex. To date its
analysis is empirical in nature and
hence it is based on experimental data
and practical experience. More are the
simplifying assumptions, more easy will
be analysis but we will be faraway from reality.
TYPES OF FLUID FLOW
(i) Steady and Unsteady flows
(ii) Uniform and Nonuniform flows
(iii) Laminar and Turbulent flows
(iv) Compressible and Incompressible flows
(v) Rotational and Ir rotational flows
(vi) One, Two and Three dimensional flows
Sr.No. 
Type of Flow 
Definition 
Mathematicalrepresentation 
1. 
UniformFlow 
When properties ofthe fluid do not vary with distance (position),(When properties gradient is zero),flow is uniform.

velocity gradientdu / dx =0

2. 
NonUniformFlow 
When properties of thefluid vary with distance(Position),(When properties gradient is not zero), flowis non uniform. 
velocity gradientdu / dx ≠0

3. 
SteadyFlow 
When properties of thefluid do not vary withtime (rate of change),itis steady flow. 
du / dt =0 i.e.rate of change =0

4. 
UnsteadyFlow 
When properties of thefluid vary with time, it isunsteady flow 
du / dt ≠0 i.e.rate of change ≠0

5. 
Uniform SteadyFlow 
When properties ofthe fluid do not varywith time as well aswith distance (position),it is called a Steadyuniform flow. 
du /dt =0 and du/dx=0dp /dt =0 and dp/dx=0dµ /dt =0 and dµ/dx=0dρ/dt =0 and dρ/dx=0 
6. 
NonUniform Steady Flow 
When propertieschange with positionbut do not changew. r. t. time, it is nonuniform steady flow. 
du /dt =0 and du/dx≠0dp /dt =0 and dp/dx≠0dµ /dt =0 and dµ/dx≠0dρ/dt =0 and dρ/dx≠0 
7. 
Uniform un Steady Flow 
When properties do not change with position but change with time, it is uniform non steady flow. 
du / dt ≠0, du / dx =0dp / dt ≠0,dp / dx =0dµ / dt ≠0,dµ/ dx =0dρ /dt ≠0,dρ/dx =0 
8. 
NonUniform NonSteady Flow 
When properties change with position as well as with time, it is unsteady non uniform flow. 
du /dt ≠0 and du/dx≠0dp /dt ≠0 and dp/dx≠0dµ /dt ≠0 and dµ/dx≠0dρ /dt ≠0 and dρ/dx≠0 
Sr. No. 
Type of Flow 
Definition 
Application 
1. 
One Dimensional Flow

When two velocity components are negligible 
fullydeveloped flows in longuniform pipes andopenchannels in whichvelocity is uniform acrossthe pipe crosssection 
2. 
2Dimensional

When one velocity components is negligible 
flow past a long structure / Flowover a long weir/Flow pastan antenna 
3. 
3Dimensional 
When all the three velocity components are equally important 
Actual flow anywhere andeverywhere 
4. 
Compressible flow 
When there is a change in density with pressure 
d ρ/dp ≠0, Applicableto flow of gases and vapors 
5. 
Incompressible flow 
When there is a no change in density with pressure 
d ρ/dp =0, Applicableto flow of liquids,Applicable for gaseswhen Mach No < 0.3

6. 
Viscous flow

When viscosity effect is predominant 
All fluids have significantviscosity except water,air and kerosene 
7. 
Nonviscous 
When viscosity effect is negligible

Flow of water, air andkerosene 
8. 
External flow 
When flow is on the outer boundary of an object

Flow external to acylinder, sphere, aerofoil,flow in a boundary layer 
9. 
Internal Flow

When flow is within some boundary which may be circular, rectangular or any other cross section 
Flow through a pipe/ tube,flow in a duct, Flow throughhydraulic machines 
10. 
Laminar flow 
Fluid layers are flowing parallel to each other 
(i) In a rough pipe, Re < 2100

11. 
Turbulent Flow 
Fluid layers are crossing to each other and are in disorder 
(i) In a rough pipe,Re > 4000 (ii) In a smooth pipe,Re >10000

12. 
Subcritical flow 
flow in a channel where gravity forces are predominant 
Froude Number =Fr = V/(gD)^{0.5}

13. 
Critical flow 
flow in a channel where gravity forces are predominant 
Fr = 1 
14. 
Super critical flow 
flow in a channel where gravity forces are predominant 
Fr > 1 
COMPRESSIBLE AND INCOMPRESSIBLE FLOW
Salient features of a compressible flow
Ludwig Prandtl found the following features linked with the compressible flow.

Boundary layer

Supersonic shock waves

wind tunnels have supersonic flow

Design of nozzles with supersonic flow.
TABLE: Comparison of Compressible and Incompressible Flow
Sr. No. 
Compressible flow 
Incompressible flow 
1. 
Density changes with pressure or temperature or with both 
Density is constant. 
2. 
Found in vapors and gases 
Found in liquids. Also found in gases also as long as Mach Number is ≤ 0.3 
3. 
Variables are velocity, pressure, density, temperature and change in entropy 
Variables are only pressure and velocity 
4. 
Equations used are continuity, momentum, energy and equation of state, change of entropy 
Equations used are continuity and momentum 
5. 
Continuity equationdρ/ρ + dA/A + dV/V =0, orρ1 A1 V1 = ρ2 A2 V2 
Continuity equationA1V1 = A2V2 
6. 
Momentum eq. ∫dp/ρ + v^{2}/2 =constant 
Momentum eq. ∫dp/ρ + v^{2}/2 =constant 
7. 
Energy eq. dp/ρ + V dV +g dz = 0 p1 + ρV1^{2}_{ }/2 = p2 + ρ V2^{2}/2 (Bernoulli’s Equation) 
Not applicable 
8. 
Equation of statedp/p –dρ/ρ –dT/T =0 
Not applicable 
9. 
Equation of change of entropyds=Cp_{ (}dT/T) — R dp/p 
Not applicable 
10. 
Analysis is complex, cumbersome and time consuming because of more number of unknowns. 
Analysis is simple 
11. 
Mathematically ∂ρ/∂p ≠0 
Mathematically ∂ρ/∂p =0 
12. 
Best way to analyze is to use Mach number 
Mach number is not of much use 
13. 
Mach number = velocity of flow/velocity of sound 
Mach number = velocity of flow/velocity of sound 
14. 
M ≥ 0.3 
M ≤ 0.3 
15. 
Study of compressible flow is called Gas Dynamics 
Called as incompressible flow 
16. 
Formation of waves is there. 
No waves formation 
17. 
Found in gas flow through nozzles, orifices, Venturimeters, compressors, turbines, airplanes, projectiles, missiles, rockets, space air crafts, water hammer, 
Mainly found in liquids. Also in gases with M ≤ 0.3 
18. 
The stagnation values (at zero velocity) p _{o}, T_{o}, ρ_{o} and h_{0} are useful reference conditions in an ISENTROPIC compressible flow 
Not applicable 
19. 
P_{o} = p[1 + ((γ –1) /2)M^{2}]^{((γ / (γ—1))} 
Not applicable 
20. 
T_{o} = T[1 + ((γ –1) /2)M^{2}] 
Not applicable 
21. 
ρ_{o} = ρ[1 + ((γ –1) /2)M^{2}]^{((1 / (γ—1))} 
Not applicable 
22. 
h_{o} = h + v^{2}/2 
Not applicable 
23. 
Uses both Lagrangian and Euler approaches and hence becomes very complex 
Uses only Lagrangian approach and is thus simpler 
24. 
Mathematically dρ /ρ ≥ 5 % 
Mathematically dρ/ρ ≤ 5 % 
25. 
Compressibility effect is considered. Z = p/(ρ R _{gas} T) 
Compressibility effect is neglected 
Methods to Study Gas Dynamics
1. Model experiments in a wind tunnel
2. Shock tubes using optical techniques
Computational Fluid Dynamics
It analysis the compressible flow. It uses supercomputers to analyze a variety of geometries and flow characteristics in a compressible flow. Both internal and external compressible flows can be evaluated. Computational fluid dynamics is an inexpensive alternative to experimental studies.
Assumptions Used in Compressible Flow

Fluid flow as a continuous substance. There are no voids or impurities in it.

There is noslip condition. In most cases, the velocity of solid surface is zero. Because of no slip condition, flow becomes viscous and a boundary layer is developed.

In an incompressible fluid flow, pressure and velocity are two unknown parameters. These are solved by using two equations, the continuity and linear momentum conservation equations. In compressible flow, pressure, velocity, density and temperature are four unknown variables. This requires the use of two more equations i.e. the conservation of energy equation and the equation of state.

Compressible fluid dynamics uses both Lagrangian and Eulerian frame of references because of its complex nature. The Lagrangian approach follows a particular particle or a group of particles of fixed identity. The Eulerian reference frame uses a fixed control volume that fluid can flow through.
NORMAL SHOCK IN A COMPRESSIBLE FLUID FLOW
When the flow passes from a supersonic to subsonic in a SMALL distance, the velocity decreases suddenly and pressure rises sharply. This sudden pressure rise is a normal to the pipe surface and is called the NORMAL SHOCK. It happens only in a compressible flow (gas flow). The vice versa is not applicable i.e. there is no shock wave from subsonic to super sonic flow. These shock waves are perpendicular to the flow. Shock waves are highly localized IRREVERSIBILITIES in a compressible fluid (gas flow) flow. These are highly undesirable and should be avoided as far as possible.
Shock wave occurs when flow is changing from supersonic to subsonic in a compressible flow (air/gas flow) over a very small (molecular) distance. There is a sudden increase in pressure, density, temperature and entropy when a shock is formed.
A shock wave is a moving disturbance. When a disturbance moves faster than the speed of sound in a fluid, it is a shock wave. A shock wave carries energy, and can propagate through a medium. It is characterized by an ABRUPT AND INSTANTANEOUS CHANGE in temperature, pressure, density, entropy, velocity and Mach number of the medium (fluid). It is normal to the flow direction and is thus called a normal shock.
A sound wave, similar to a shock wave, is heard as the familiar “thud” when a supersonic aircraft moves in the air. A shock wave is similar to a sound wave created by an object traveling through the air faster than the speed of sound. In smooth flight, the shock wave starts at the nose of the aircraft and ends at the tail. There is a rise in pressure at the front nose of the aircraft and pressure decreases steadily and becomes a negative pressure at the tail of the aircraft. Suddenly there is a return to normal pressure after the object passes. This is called Normalwave.
Normal Shock, Fanno Line and Rayleigh Line in a Compressible Flow (Gas FLOW)
FANNO LINE
Fanno flow is the locus of points with the same mass flux (G=constant) and the same stagnation enthalpy (h^{0}=constant). Stagnation means at zero velocity. Fanno lines are thus lines of CONSTANT STAGNATION TEMPERATURE, and hence of CONSTANT STAGNATION ENTHALPY:
Fanno flow is for one dimensional adiabatic flow (dq=0) in a duct of constant area with FRICTION.
RAYLEIGH LINE
Rayleigh line is a locus of points with same impulse pressure and same mass flux. It represents states of constant mass flux (flow per unit area) when heat is transferred to or from a gas (dq ≠0). It is a non adiabatic flow line.
FANNO LINE AND RAYLEIGH LINE
Fanno lines and Rayleigh lines are often considered together. These lines are represented on enthalpy entropy chart. The intersection of Fanno line and Rayleigh line represents the end points in a normal shock for the same mass flux ‘G’. Each point on the Fanno line has a different Mach number.
Each point on the Rayleigh line has a different Mach number.
Even the sonic points ( M=1) are different on these lines. But these lines do intersect at two points. One of these intersecting point lies on supersonic region while other lies on subsonic region. Thus line joining these points represents the normal shock wave. FLOW WITH A CONSTANT AREA DUCT CAN SWITCH BETWEEN THE FANNO AND RAYLEIGH LINE.
https://www.mesubjects.net/wpadmin/post.php?post=7698&action=edit FM introduction