FLUID FLOW
THIRD SEMESTER
5 MARKS QUSTIONS
1. TERMINOLOGY IN FLUID DYNAMICS
The concept of pressure is central to the study of both fluid statics and fluid
dynamics. A pressure can be identified for every point in a body of fluid,
regardless of whether the fluid is in motion or not. Pressure can
be measured using an aneroid, Bourdon tube, mercury column, or various other
methods.
Some of the terminology that is necessary in the study of fluid dynamics is not
found in other similar areas of study. In particular, some of the terminology used
in fluid dynamics is not used in fluid statics.
 Terminology in incompressible fluid dynamics
The concepts of total pressure and dynamic pressure arise from Bernoulli's
equation and are significant in the study of all fluid flows. (These two pressures
are not pressures in the usual sense—they cannot be measured using an aneroid,
Bourdon tube or mercury column.) To avoid potential ambiguity when referring
to pressure in fluid dynamics, many authors use the term static pressure to
distinguish it from total pressure and dynamic pressure. Static pressure is
identical to pressure and can be identified for every point in a fluid flow field.
A point in a fluid flow where the flow has come to rest (i.e. speed is equal to zero
adjacent to some solid body immersed in the fluid flow) is of special significance.
It is of such importance that it is given a special name—a stagnation point. The
static pressure at the stagnation point is of special significance and is given its
own name—stagnation pressure. In incompressible flows, the stagnation pressure
at a stagnation point is equal to the total pressure throughout the flow field.
 Terminology in compressible fluid dynamics
In a compressible fluid, such as air, the temperature and density are essential
when determining the state of the fluid. In addition to the concept of total
pressure (also known as stagnation pressure), the concepts of total (or
stagnation) temperature and total (or stagnation) density are also essential in any
study of compressible fluid flows.
2. VISCOUS VS INVISCID FLOW
Viscous problems are those in which fluid friction has significant effects on the
fluid motion.
The Reynolds number, which is a ratio between inertial and viscous forces, can be
used to evaluate whether viscous or inviscid equations are appropriate to the
problem.
Stokes flow is flow at very low Reynolds numbers, Re<<1, such that inertial forces
can be neglected compared to viscous forces.
On the contrary, high Reynolds numbers indicate that the inertial forces are more
significant than the viscous (friction) forces. Therefore, we may assume the flow
to be an inviscid flow, an approximation in which we neglect viscosity completely,
compared to inertial terms.
This idea can work fairly well when the Reynolds number is high. However, certain
problems such as those involving solid boundaries, may require that the viscosity
be included. Viscosity often cannot be neglected near solid boundaries because
the no-slip condition can generate a thin region of large strain rate (known
as Boundary layer) which enhances the effect of even a small amount of viscosity,
and thus generating vorticity. Therefore, to calculate net forces on bodies (such as
wings) we should use viscous flow equations. As illustrated by d'Alembert's
paradox, a body in an inviscid fluid will experience no drag force. The standard
equations of inviscid flow are the Euler equations. Another often used model,
especially in computational fluid dynamics, is to use the Euler equations away
from the body and the boundary layer equations, which incorporates viscosity, in
a region close to the body.
The Euler equations can be integrated along a streamline to get Bernoulli's
equation. When the flow is everywhere irrotational and inviscid, Bernoulli's
equation can be used throughout the flow field. Such flows are called potential
flows.
3.COMPRESSIBLE FLOW PHENOMENA
Two of the most distinctive phenomena which occur in compressible are the
possibility of choked flow(see Internal Flows) and the presence of acoustic waves,
which may also be referred to as either compression or expansion waves,
depending on whether they lead to an increase or decrease in pressure[1].
 Shock Waves
Shock waves are one of the most common examples of compressible flow
phenomena. A shock is characterised by a discontinuous change in the
thermodynamic properties. In one dimensional flows, shock waves can form
when a series of compression waves coalesce, or when a membrane separating
two regions of differing pressure is suddenly removed. This is the technique often
used to produce shock waves in shock tubes (see Shock Tubes).
In two and three dimensional supersonic flows, oblique shock waves occur as a
result of a change in direction of the flow. A classic example of these shock waves
are those shock waves that form off the nose of a supersonic aircraft.
 Aerodynamics
Aerodynamics is a subfield of fluid dynamics and gas dynamics, and is primarily
concerned with obtaining the forces that air exerts on an object. For Mach
numbers greater than about 0.3, density changes are significant, and the flow
should be considered compressible for an accurate representation of reality.
20 MARKS QUS
1.EQUATIONS OF FLUID DYNAMICS
The foundational axioms of fluid dynamics are the conservation laws,
specifically, conservation of mass, conservation of linear momentum (also known
as Newton's Second Law of Motion), and conservation of energy (also known
as First Law of Thermodynamics). These are based on classical mechanics and are
modified in quantum mechanics and general relativity. They are expressed using
theReynolds Transport Theorem.
In addition to the above, fluids are assumed to obey the continuum assumption.
Fluids are composed of molecules that collide with one another and solid objects.
However, the continuum assumption considers fluids to be continuous, rather
than discrete. Consequently, properties such as density, pressure, temperature,
and velocity are taken to be well-defined at infinitesimally small points, and are
assumed to vary continuously from one point to another. The fact that the fluid is
made up of discrete molecules is ignored.
Compressible vs incompressible flow
All fluids are compressible to some extent, that is, changes in pressure or
temperature will result in changes in density. However, in many situations the
changes in pressure and temperature are sufficiently small that the changes in
density are negligible. In this case the flow can be modeled as an incompressible
flow. Otherwise the more general compressible flow equations must be used.
Mathematically, incompressibility is expressed by saying that the density ρ of
a fluid parcel does not change as it moves in the flow field, i.e.,
Steady vs unsteady flow
When all the time derivatives of a flow field vanish, the flow is considered to be
a steady flow. Steady-state flow refers to the condition where the fluid properties
at a point in the system do not change over time. Otherwise, flow is called
unsteady. Whether a particular flow is steady or unsteady, can depend on the
chosen frame of reference. For instance, laminar flow over asphere is steady in
the frame of reference that is stationary with respect to the sphere. In a frame of
reference that is stationary with respect to a background flow, the flow is
unsteady.
Turbulent flows are unsteady by definition. A turbulent flow can, however,
bestatistically stationary. According to Pope:[3]
Laminar vs turbulent flow
Turbulence is flow characterized by recirculation, eddies, and
apparent randomness. Flow in which turbulence is not exhibited is calledlaminar.
It should be noted, however, that the presence of eddies or recirculation alone
does not necessarily indicate turbulent flow—these phenomena may be present
in laminar flow as well. Mathematically, turbulent flow is often represented via
a Reynolds decomposition, in which the flow is broken down into the sum of
an average component and a perturbation component.
It is believed that turbulent flows can be described well through the use of
the Navier–Stokes equations. Direct numerical simulation(DNS), based on the
Navier–Stokes equations, makes it possible to simulate turbulent flows at
moderate Reynolds numbers. Restrictions depend on the power of the
computer used and the efficiency of the solution algorithm. The results of DNS
have been found to agree well with experimental data for some flows.[4]
Newtonian vs non-Newtonian fluids
Sir Isaac Newton showed how stress and the rate of strain are very close to
linearly related for many familiar fluids, such as water andair. These Newtonian
fluids are modeled by a coefficient called viscosity, which depends on the specific
fluid.
However, some of the other materials, such as emulsions and slurries and some
visco-elastic materials (e.g. blood, some polymers), have more complicated nonNewtonian stress-strain behaviours. These materials include sticky liquids such
as latex, honey, and lubricants which are studied in the sub-discipline of rheology.
Subsonic vs transonic, supersonic and hypersonic flows
While many terrestrial flows (e.g. flow of water through a pipe) occur at low mach
numbers, many flows of practical interest (e.g. in aerodynamics) occur at high
fractions of the Mach Number M=1 or in excess of it (supersonic flows). New
phenomena occur at these Mach number regimes (e.g. shock waves for
supersonic flow, transonic instability in a regime of flows with M nearly equal to
1, non-equilibrium chemical behavior due to ionization in hypersonic flows) and it
is necessary to treat each of these flow regimes separately.
Magnetohydrodynamics
Main article: Magnetohydrodynamics
Magnetohydrodynamics is the multi-disciplinary study of the flow of electrically
conducting fluids in electromagnetic fields. Examples of such fluids
include plasmas, liquid metals, and salt water. The fluid flow equations are solved
simultaneously with Maxwell's equationsof electromagnetism.
Other approximations
There are a large number of other possible approximations to fluid dynamic
problems. Some of the more commonly used are listed below.

The Boussinesq approximation neglects variations in density except to
calculate buoyancy forces. It is often used in freeconvection problems where
density changes are small.


Lubrication theory and Hele-Shaw flow exploits the large aspect ratio of the
domain to show that certain terms in the equations are small and so can be
neglected.
Slender-body theory is a methodology used in Stokes flow problems to
estimate the force on, or flow field around, a long slender object in a viscous
fluid.
2. TYPES OF FLUID FLOW
 Cavitation
Cavitation is the formation and then immediate implosion of cavities in a liquid –
i.e. small liquid-free zones ("bubbles") – that are the consequence of forces acting
upon the liquid.[1] It usually occurs when a liquid is subjected to rapid changes
of pressurethat cause the formation of cavities where the pressure is relatively
low.
Cavitation is a significant cause of wear in some engineering contexts. When
entering high pressure areas, cavitation bubbles that implode on a metal surface
cause cyclic stress. This results in surface fatigue of the metal causing a type of
wear also called "cavitation". The most common examples of this kind of wear are
pump impellers and bends when a sudden change in the direction of liquid
occurs. Cavitation is usually divided into two classes of behaviour: inertial (or
transient) cavitation and non-inertial cavitation.
 Compressible flow
Subsonic Aerodynamics
Due to the complexities of compressible flow theory, it is often easier to calculate
the incompressible flow characteristics first, and then employ a correction factor
to obtain the actual flow properties. Several correction factors exist with varying
degrees of complexity and accuracy.
[edit]Prandtl–Glauert transformation
The Prandtl-Glauert transformation is found by linearizing the potential equations
associated with compressible, inviscid flow. The Prandtl–Glauert transformation
or Prandtl–Glauert rule (also Prandtl–Glauert–Ackeret rule) is an approximation
function which allows comparison of aerodynamical processes occurring at
different Mach numbers. It was discovered that the linearized pressures in such a
flow were equal to those found from incompressible flow theory multiplied by a
correction factor. This correction factor is given below. [3]:
where



cp is the compressible pressure coefficient
cp0 is the incompressible pressure coefficient
M is the Mach number.
 Couette flow
Mathematical description
Couette flow is frequently used in undergraduate physics and engineering courses
to illustrate shear-driven fluid motion.[1] The simplest conceptual configuration
finds two infinite, parallel plates separated by a distance h. One plate, say the top
one, translates with a constant velocity u0 in its own plane. Neglecting pressure
gradients, the Navier-Stokes equations simplify to
Constant shear
A notable aspect of this model is that shear stress is constant throughout the flow
domain.[2] In particular, the first derivative of the velocity, u0 / h, is constant. (This
is implied by the straight-line profile in the figure.) According to Newton's Law of
Viscosity (Newtonian fluid), the shear stress is the product of this expression and
the (constant) fluid viscosity.
 Free molecular flow
Free molecular flow describes the fluid dynamics of gas where the mean free
path of the molecules is larger than the size of the chamber or of the object under
test. For tubes/objects of the size of several cm, these means pressures well
below 10-3 torr. This is also called the regime of high vacuum.
 Incompressible flow
Relation to compressibility
 In some fields, a measure of the incompressibility of a flow is the change
in density as a result of the pressure variations. This is best expressed in
terms of the compressibility

 If the compressibility is acceptably small, the flow is considered to be
incompressible.
Relation to solenoidal field
 An incompressible flow is described by a velocity field which
is solenoidal. But a solenoidal field, besides having a zero divergence,
also has the additional connotation of having non-zero curl (i.e.,
rotational component).
 Otherwise, if an incompressible flow also has a curl of zero, so that it is
also irrotational, then the velocity field is actually Laplacian.
 Inviscid flow
Reynolds number
 The assumption of inviscid flow is generally valid where viscous forces
are small in comparison to inertial forces. Such flow situations can be
identified as flows with a Reynolds number much greater than one. The
assumption that viscous forces are negligible can be used to simplify
the Navier-Stokes solution to the Euler equations.
 The Euler equation governing inviscid flow is:

 Isothermal flow
Isothermal flow is a model of compressible fluid flow whereby the flow remains
at the same temperature while flowing in a conduit.[1] In the model, heat
transferred through the walls of the conduit is offset by frictional heating back
into the flow. Although the flowtemperature remains constant, a change in
stagation temperature occurs because of a change in velocity. The interesting part
of this flow is that the flow is choked at
and not at Mach number equal to
one as in the case of many other model such as Fanno flow. This fact applies to
real gases as well as ideal gases.
For an important practical case of a gas flow throw a long tube the model has an
applicability in situations which occurs in a relatively long distance and where
heat transfer is relatively rapid so that the temperature can be treated, for
engineering purposes, as a constant. This model has also applicability as upper
boundary to Fanno flow.
3. MISCELLANEOUS
 Isosurface
An isosurface is a three-dimensional analog of an isoline. It is a
surface that represents points of a constant value (e.g. pressure,
temperature, velocity, density) within a volume of space; in other
words, it is a level set of a continuous function whose domain is
3D-space.
Isosurfaces are normally displayed using computer graphics, and
are used as data visualization methods in computational fluid
dynamics (CFD), allowing engineers to study features of a fluid
flow (gas or liquid) around objects, such as aircraft wings. An
isosurface may represent an individual shock
wave in supersonic flight, or several isosurfaces may be generated
showing a sequence of pressure values in the air flowing around a
wing. Isosurfaces tend to be a popular form of visualization for
volume datasets since they can be rendered by a simple polygonal
model, which can be drawn on the screen very quickly.
 Rotating tank.
A rotating tank is a deviceused for fluid dynamics experiments. Typically cylinders
filled with water on a rotating platform, the tanks can be used in various ways to
simulate the atmosphere or ocean.
For example, a rotating tank with an ice bucket in the center can represent the
Earth, with a cold pole simulated by the ice bucket. Just as in the
atmosphere, eddies and a westerly jetstream form in the water.
 Sound barrier
The sound barrier, in aerodynamics, is the point at which an aircraft moves
from transonicto supersonic speed. The term, which occasionally has other
meanings, came into use during World War II, when a number of aircraft started
to encounter the effects ofcompressibility, a collection of several unrelated
aerodynamic effects that "struck" their planes like an impediment to further
acceleration. By the 1950s, new aircraft designs routinely "broke" the sound
barrier.
 Beta plane
. The advantage of the beta plane approximation over more accurate
formulations is that it does not contribute nonlinear terms to the dynamical
equations; such terms make the equations harder to solve. The name 'beta
plane' derives from the convention to denote the linear coefficient of
variation with the Greek letter β.
The beta plane approximation is useful for the theoretical analysis of many
phenomena in geophysical fluid dynamics since it makes the equations
much more tractable, yet retains the important information that the
Coriolis parameter varies in space. In particular,Rossby waves, the most
important type of waves if one considers large-scale atmospheric and
oceanic dynamics, depend on the variation of f as a restoring force; they do
not occur if the Coriolis parameter is approximated only as a constant.
 Immersed boundary method
The immersed boundary method is an approach – in computational fluid
dynamics – to model and simulate mechanical systems in which elastic structures
(or membranes) interact with incompressible fluid flows. Treating the coupling
(the elastic boundary changes the flow of the fluid and the fluid moves the elastic
boundary simultaneously) of the structure deformations and the fluid flow poses
a number of challenging problems for numerical simulations. In the immersed
boundary method approach the fluid is represented in anEulerian coordinate
frame and the structures in a Lagrangian coordinate frame. For Newtonian
fluids governed by the Navier–Stokes equations the immersed boundary method
fluid equations are
 Bridge scour
Bridge scour is the removal of sediment such as sand and rocks from
around bridgeabutments or piers. Scour, caused by swiftly moving water, can
scoop out scour holes, compromising the integrity of a structure
Areas affected by scour
.
Water normally flows faster around piers and abutments making them
susceptible to local scour. At bridge openings, contraction scour can occur when
water accelerates as it flows through an opening that is narrower than the
channel upstream from the bridge. Degradation scour occurs both upstream and
downstream from a bridge over large areas. Over long periods of time, this can
result in lowering of the stream bed.[2]
Causes
Stream channel instability resulting in river erosion and changing angles-of-attack
can contribute to bridge scour. Debris can also have a substantial impact on
bridge scour in several ways. A build-up of material can reduce the size of the
waterway under a bridge causing contraction scour in the channel. A build-up of
debris on the abutment can increase the obstruction area and increase local
scour.
 Keulegan–Carpenter number
In fluid dynamics, the Keulegan–Carpenter number, also called the period
number, is a dimensionless quantity describing the relative importance of
thedrag forces over inertia forces for bluff objects in an oscillatory fluid
flow. Or similarly, for objects that oscillate in a fluid at rest. For small
Keulegan–Carpenter number inertia dominates, while for large numbers
the (turbulence) drag forces are important.
The Keulegan–Carpenter number KC is defined as:[1]
where:



V is the amplitude of the flow velocity oscillation (or the amplitude of the
object's velocity, in case of an oscillating object),
T is the period of the oscillation, and
L is a characteristic length scale of the object, for instance the diameter for
acylinder under wave
4. FLUID PHENOMENA
 Boundary layer
n physics and fluid mechanics, a boundary layer is the layer of fluid in the
immediate vicinity of a bounding surface where the effects of viscosity are
significant. In the Earth's atmosphere, the planetary boundary layer is the air layer
near the ground affected by diurnal heat, moisture or momentum transfer to or
from the surface. On an aircraft wing the boundary layer is the part of the flow
close to the wing, where viscous forces distort the surrounding non-viscous flow.
Aerodynamics
The aerodynamic boundary layer was first defined by Ludwig Prandtl in a paper
presented on August 12, 1904 at the third International Congress of
Mathematicians in Heidelberg, Germany. It simplifies the equations of fluid flow
by dividing the flow field into two areas: one inside the boundary layer,
dominated by viscosity and creating the majority of drag experienced by the
boundary body; and one outside the boundary layer, where viscosity can be
neglected without significant effects on the solution. This allows a closed-form
solution for the flow in both areas, a significant simplification of the fullNavier–
Stokes equations. The majority of the heat transfer to and from a body also takes
place within the boundary layer, again allowing the equations to be simplified in
the flow field outside the boundary layer
 Coandă effect
Causes
The Coandă effect is a result of entrainment of ambient fluid around the fluid jet.
When a nearby wall does not allow the surrounding fluid to be pulled inwards
towards the jet (i.e. to be entrained), the jet moves towards the wall instead. The
fluid of the jet and the surrounding fluid should be essentially the same substance
(a gas jet into a body of gas or a liquid jet into a body of liquid). In one application,
a jet of air is blown over the upper surface of an airfoil, which can have a strong
influence on the overall lift, especially at high angles of attack when the flow
would otherwise separate (stall).
 Convection cell
A convection cell is a phenomenon of fluid dynamics that occurs in situations
where there are density differences within a body of liquid or gas. The convection
usually requires a gravitational field but in microgravity experiments, thermal
convection has been observed without gravitational effects being needed
 Process
A rising body of fluid typically loses heat because it encounters a cold surface;
because it exchanges heat with colder liquid through direct exchange; or in the
example of the Earth's atmosphere, because it radiates heat. At some point, the
fluid becomes denser than the fluid underneath it, which is still rising. Since it
cannot descend through the rising fluid, it moves to one side. At some distance,
its downward force overcomes the rising force beneath it, and the fluid begins to
descend. As it descends, it warms again through surface contact or conductivity
and the cycle repeats itself
 Hydrodynamic stability
In fluid dynamics, hydrodynamic stability is the field which analyses the stability
and the onset of instability of fluid flows
 Rossby wave
Atmospheric Rossby waves are giant meanders in high-altitude winds that are a
major influence on weather.[1] They are not to be confused with oceanic Rossby
waves, which move along the thermocline: that is, the boundary between the
warm upper layer of the ocean and the cold deeper part of the ocean.
 Atmospheric waves
Atmospheric Rossby waves emerge due to shear in rotating fluids, so that
the Coriolis force changes along the sheared coordinate.
Inplanetary atmospheres, they are due to the variation in the Coriolis
effect with latitude. The waves were first identified in the Earth's atmosphere in
1939 by Carl-Gustaf Arvid Rossby who went on to explain their motion.
One can identify a Rossby wave in that its phase velocity (that of the wave crests)
always has a westward component. However, the wave's group
velocity (associated with the energy flux) can be in any direction. In general,
shorter waves have an eastward group velocity and long waves a westward group
velocity.
 Shock wave
A shock wave (also called shock front or simply "shock") is a type of propagating
disturbance. Like an ordinary wave, it carries energy and can propagate through a
medium (solid, liquid, gas or plasma) or in some cases in the absence of a material
medium, through a field such as the electromagnetic field. Shock waves are
characterized by an abrupt, nearly discontinuous change in the characteristics of
the medium.[1] Across a shock there is always an extremely rapid rise
in pressure, temperature and density of the flow. In supersonic flows, expansion
is achieved through an expansion fan. A shock wave travels through most media
at a higher speed than an ordinary wave.
 Soliton.
In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave
packetor pulse) that maintains its shape while it travels at constant speed.
Solitons are caused by a cancellation of nonlinear and dispersive effects in the
medium. (The term "dispersive effects" refers to a property of certain systems
where the speed of the waves varies according to frequency.) Solitons arise as the
solutions of a widespread class of weakly nonlinear dispersive partial differential
equations describing physical systems. The soliton phenomenon was first
described by John Scott Russell (1808–1882) who observed a solitary wave in
the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and
named it the "Wave of Translation".
.
.