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FM-1, L # 07

FM-1,L # 01

Fluid Mechanics-1

Prepared by
Prof: Abdul Samad
Mechanical Engineering department.
2015
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Introduction
All real fluids are viscous in nature the fluid viscosity
produces tangential forces or shear forces in a moving
fluid. These tangential forces acts as a friction force and
tend to retard the motion of fluid particles, consequently
dissipation/degradation in the mechanical energy. Mostly
viscosity effects have to be considered when dealing with
fluid flow in pipes or conduits.
Laminar flow
Also known as
streamline flow
Occurs when the
fluid flows in
parallel layers,
with no disruption
between the layers
The opposite of
turbulent flow
(rough)
Laminar flow
Turbulent
Laminar flow over a flat
Flow
and horizontal surface can
be pictured as consisting
of parallel and thin layers

Layers slide over each Laminar Flow

other, thus the name
‘streamline’ or smooth.
The paths are regular and
there are no fluctuations
Laminar flow
 Characteristics:
fluid moves slowly
viscosity is relatively high
flow channel is relatively small
No slip at boundaries
Small diameter
Low velocity
Definite path
Path lines are always parallel to each other.
Examples of laminar flow
Under ground flow
Movement of blood in arteries
Rise of water in plants through roots.
Turbulent flow
Usually occurs when the
liquid is moving fast
The flow is ‘chaotic’ and there
are irregular fluctuations
Includes:
high momentum convection
rapid variation of pressure
and velocity of the fluid
Turbulent Flow
The speed of the fluid at a point is continuously
undergoing changes in both magnitude and direction.
Reynolds’ Experiment
Reynold’s number
The Reynold’s number can be used to determine if a
flow is laminar, transient or turbulent

Laminar when Re < 2300

Turbulent when Re > 4000
Transient when 2300 < Re < 4000

Spermatozoa 1×10−4
Blood flow in brain 1×102
Blood flow in aorta 1×103
Reynold’s Experiment
In 1883, Osborne Reynolds demonstrated that there
are two distinctly different types of flow by injecting a
very thin stream of colored fluid having the same
density of water into a large transparent tube through
which water is flowing. And from the feature of
streaming this dye fluid , Reynold give a number can
be considered as a boundary between flow faces , this
number is a function of , flow velocity , fluid density ,
pipe diameter , and fluid viscosity , where ;
R= f (V , ρ , υ (or μ ) , D ) …………………….. (1) and then ,
R= VDρ/μ or R = VD/υ ; R= Reynolds No., μ =
dynamic viscosity , υ = kinematic viscosity .
where, Re = Reynolds number V = velocity of fluid
(m/s) Dh = hydraulic diameter (m) μ (mu) = dynamic
viscosity of fluid (N.s/m2 ) ν (nu) = kinematic viscosity
of fluid (m2 /s) ρ (rho) = density (kg/m3 ) The
hydraulic diameter (different than h
Reynolds Number

The transition from laminar to turbulent flow

depends on the geometry, surface roughness, flow
velocity, surface temperature, and type of fluid,
among other things. After exhaustive experiments
in the 1880s, Osborne Reynolds discovered that
the flow regime depends mainly on the ratio of
inertial forces to viscous forces in the fluid. This
ratio is called the Reynolds number and is
expressed for internal flow in a circular pipe as
Examples of turbulence
Oceanic and atmospheric layers and ocean currents
External flow of air/water over vehicles such as
cars/ships/submarines
In racing cars, e.g. leading car causes understeer at fast
corners
Turbulence during air-plane’s flight
Flow of most liquids through pipes
Reynold’s number
Flow in a pipe or liquid
 p is the density of the fluid
 V is the mean fluid velocity
 D is the diameter
Dynamic Pressure
 Q is the volumetric flow rate

 μ is the dynamic viscosity of the fluid

Shearing Stress
 v is the kinematic velocity of the fluid
 A is the pipe cross-sectional area.
Fluid flow in circular and noncircular pipes is commonly
encountered in practice. The hot and cold water that we
use in our homes is pumped through pipes. Water in a city
is distributed by extensive piping networks. Oil and
natural gas are transported hundreds of miles by large
pipelines. Blood is carried throughout our bodies by
arteries and veins. The cooling water in an engine is
transported by hoses to the pipes in the radiator where it
is cooled as it flows. Thermal energy in a hydronic space
heating system is transferred to the circulating water in
the boiler, and then it is transported to the desired
locations through pipes.
Fluid flow is classified as external and internal,
depending on whether the fluid is forced to flow
over a surface or in a conduit. Internal and
external flows exhibit very different
characteristics. In this chapter we consider
internal flow where the conduit is completely
filled with the fluid, and flow is driven primarily
by a pressure difference. This should not be
confused with open-channel flow where the
conduit is partially filled by the fluid and thus the
flow is partially bounded by solid surfaces, as in
an irrigation ditch, and flow is driven by gravity
alone.
We start this chapter with a general physical
description of internal flow and the velocity
boundary layer. We continue with a discussion of
the dimensionless Reynolds number and its
physical significance.
We then discuss the characteristics of flow inside
pipes and introduce the pressure drop correlations
associated with it for both laminar and turbulent
flows. Then we present the minor losses and
determine the pressure drop and the sizes
requirements for real-world piping systems.
The terms pipe, duct, and conduit are usually used
interchangeably for flow sections. In general, flow
sections of circular cross section are referred to as
pipes (especially when the fluid is a liquid), and flow
sections of noncircular
cross section as ducts (especially when the fluid is a
gas). Small diameter pipes are usually referred to as
tubes. Given this uncertainty, we will use more
descriptive phrases (such as a circular pipe or a
rectangular duct) whenever necessary to avoid any
misunderstandings.
 LAMINAR AND TURBULENT FLOWS

If you have been around smokers, you probably noticed that the cigarette
smoke rises in a smooth plume for the first few centimeters and then
starts fluctuating randomly in all directions as it continues its rise. Other
plumes behave similarly (Fig. 8–3). Likewise, a careful inspection of flow
in a pipe reveals that the fluid flow is streamlined at low velocities but
turns chaotic as the velocity is increased above a critical value, as shown
in Fig. 8–4. The flow regime in the first case is said to be laminar,
characterized by smooth streamlines and highly ordered motion, and
turbulent in the second case, where it is characterized by velocity
fluctuations and highly disordered motion.
The transition from laminar to turbulent flow does not occur suddenly;
rather, it occurs over some region in which the flow fluctuates between
laminar and turbulent flows before it becomes fully turbulent. Most flows
encountered in practice are turbulent. Laminar flow is encountered when
highly viscous fluids such as oils flow in small pipes or narrow passages.
Reynolds Number

The transition from laminar to turbulent flow

depends on the geometry, surface roughness, flow
velocity, surface temperature, and type of fluid,
among other things. After exhaustive experiments
in the 1880s, Osborne Reynolds discovered that
the flow regime depends mainly on the ratio of
inertial forces to viscous forces in the fluid. This
ratio is called the Reynolds number and is
expressed for internal flow in a circular pipe as
VISCOSITY
When real fluids flow they have a certain
amount of internal friction called viscosity. It
exists in both liquids and gases and is
essentially a friction force between different
layers of fluid as they move past one another.
In liquids the viscosity is due to the cohesive
forces between the molecules whilst in gases
the viscosity is due to collisions between the
molecules.
Why is honey sticky?
Viscous fluids tend to cling to a solid
surface.
• Syrup and honey are more viscous than
water.
• Grease is more viscous than engine oils.
•
Liquids are more viscous than gases.
• Lava is an example of a very viscous
material.
Hagen–Poiseuille equation In fluid dynamics, the
Hagen–Poiseuille equation is a physical law that gives
the pressure drop in a fluid flowing through a long
cylindrical pipe. The assumptions of the equation are
that the flow is laminar viscous and incompressible and
the flow is through a constant circular cross-section that
is significantly longer than its diameter. The equation is
also known as the Hagen–Poiseuille law.
Poiseuille Flow
Steady viscous fluid flow driven by an effective pressure
gradient established between the two ends of a long
straight pipe of uniform circular cross-section is
generally known as Poiseuille flow.
Poiseuille's Law. In the case of smooth flow
(laminar flow), the volume flow rate is given by the
pressure difference divided by the viscous
resistance. This resistance depends linearly upon
the viscosity and the length, but the fourth power
dependence upon the radius is dramatically
different.
The equation which gives us the value of loss of
head due to viscosity in a laminar flow , is known
as Hagen–Poiseuille law
In non ideal fluid dynamics, the Hagen–
Poiseuille equation, also known as the
Hagen–Poiseuille law.
Poiseuille law or Poiseuille equation, is a
physical law that gives the pressure drop in
an incompressible and Newtonian fluid in
laminar flow flowing through a long
cylindrical pipe of constant cross section.
For analyzing laminar flow of an
incompressible flow through a solid
cylinder of fluid, of radius R, we consider
the equilibrium forces on a small
concentric cylindrical fluid element of
radius R. The forces inside a cylindrical
pipe due to pressure force and shear force
on it .
Equation
In standard fluid dynamics notation:
 ‫ﷲ ﻮﺍﻫﻲ‬

THANK YOU

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