



FLUID FLOW
STREAMLINE – LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER





? 
What type of fluid flow is observed? 





The above pictures show
how the effect of swirl on the flow around a sphere. The flow is from top to
bottom. The picture on the left is for zero swirl and the flow is attached on
the upstream hemisphere and separated downstream of the point of maximum
thickness. A separation bubble is formed on the downstream hemisphere and
this is a region of very slow reversed axial flow. When the swirl is
increased a separation bubble appears on the upstream hemisphere which is
shown in the middle picture. As the swirl is further increased this upstream
separation bubble grows in length and becomes increasingly unsteady and
finally developed into the unsteady spiral structure as shown in the picture
on the right. 




! ! 
There are two kinds of fluid
(liquids and gases) flow that are observed: laminar
(streamline) flow and turbulent flow. When a stream of gently
flowing fluid is diverted by the presence of a wall, the particles of fluid
do not all bounce off the wall,
most bounce off other fluid particles. Since the stream is diverted
(accelerated) the wall must be exerting a force on the fluid, and the fluid
on the wall. The origin of this force
must be that the fluid molecules bounce off one another, causing those next
to the wall to bounce off it more violently.
That means the fluid pressure
must increase near the corner. Whatever the means whereby
force is exerted on the wall, it is clear that for some parts of their motion
particles of the fluid do not travel in straight lines but in curved paths.
It turns out that it is more helpful in describing fluid flow to think of the
fluid as a continuous
substance rather than to concentrate on the motion of individual
molecules. Particles of this continuous
fluid can be considered to travel along these smooth continuous paths which
are given the name streamlines.
These streamlines can be curved or straight,
depending on the flow of the fluid. This type of motion is also called laminar flow. This continuous substance
can be regarded as being made up of bundles or tubes of streamlines (flow tubes).
The tubes have elastic properties: (a) A tensile strength (b) zero shear modulus,
which means that each streamline moves independently of any other. Streamline
motion is not the only possible kind of fluid motion. When the motion becomes too violent,
eddies and vortices occur. The motion
becomes turbulent. 







Turbulence is important
because it is a means whereby energy gets dissipated. The shape of a body
will, to some extent, decide whether it will move through a fluid in
streamline or turbulent This is very important in aeronautical engineering. Air turbulence means increased fuel consumption in aircraft, and many cunning and intricate devices are used to reduce turbulence. Shapes of marine animals, flying birds, racing cars are important to avoid turbulent flow around them. 





Transition from laminar to turbulent flow as the velocity of the
water is increased by tilting a water tank. 













! 
TURBULENT FLOW A vigorous mixing (stirring) of the fluid occurs. A complex flow pattern changes continuously with time. The velocity of the particles at each given point various chaotically with time. The erratic motion of the fluid often shows small whirlpoollike circles called eddies (eddy currents) or vortices. Eddies absorb a great deal of energy due their rotational kinetic energy. A coloured dye added to a stream will readily disperse. · A transition from laminar flow to turbulent flow occurs very suddenly as the flow rate increases. The flow becomes unstable at some critical speed. · Turbulent flow occurs when there are abrupt changes in boundary surfaces. The flow of blood through a normal artery is laminar. However, when irregularities occur the flow becomes turbulent. The noise generated by the turbulent flow can be heard with a stethoscope. · When the flow becomes turbulent there is a dramatic decrease in the volume flow rate. · When a fluid flows around an object the shape of the object is a very important parameter in determining the type of flow. 




? 
What factors determine whether a
fluid will flow in laminar or turbulent motion? 








REYNOLDS NUMBER A British scientist Osborne
Reynolds (1842 – 1912) established that the nature of the flow depends upon a
dimensionless quantity, which is now called the Reynolds number R_{e}. R_{e}
= r v L / h r
density
of fluid v average flow velocity over the cross
section of the pipe L dimension characterising a cross
section 


·
R_{e} is
not a precise physical quantity. The
quantities L and v are only typical values of size and
speed. It is often not possible even
to say which length you are talking
about. For a body moving through a
fluid it might be either length or breadth or thickness  or any other
dimension you might think of. For a
fluid flowing through a channel or a tube, it turns out to be the diameter of
the tube. ·
How easily the fluid becomes turbulent is
related to its viscosity h and
density r. ·
R_{e} is a dimensionless number [Re] º [m.s^{1}][m][kg.m^{3}][Pa.s]^{1}
º [m^{1}][kg][s^{2}][kg^{1}.m^{1}.s^{2.}m^{2}] ·
As a rule of thumb R < ~2000 laminar flow
and R >~ 2000 turbulent flow. ·



Here are some flow systems with their
Reynolds Number ·
A Sydney Harbour ferry Assume
ferries travel at a speed ~ 5 m.s^{1} and are about 20 m in length.
R ~ (5)(20)(10^{3}) / (10^{3})
~ 10^{8} It
would be almost impossible to keep the flow streamlined and so there is
considerable energy loss through turbulence. ·
Household plumbing pipes Typical household pipes are about 30 mm in
diameter and water flows at about 10 m.s^{1}. R
~
(10)(30´10^{3})(10^{3}) / (10^{3}) ~ 3´10^{5} ^{ } In this example it would be almost impossible
to keep the flow streamlined and so energy loss through turbulence must be a
serious consideration. However due to
the interplay between L and v it is easier and more desirable to
obtain streamline flow in the main pipes. ^{ } ·
The circulatory system Speed of blood v ~ 0.2 m.s^{1} Diameter of the largest blood vessel, the
aorta L ~ 10 mm Viscosity of blood probably h ~ 10^{3} Pa.s (assume same as water) R ~ (0.2)(10´10^{3})(10^{3})
/ 10^{3}) ~ 2´10^{3} It is impossible to tell. In fact the tubes are of good enough geometrical structure that turbulence very rarely occurs, and so the heart is not called upon to supply energy that is dissipated through turbulence.^{} ·
Spermatozoa swimming Typically length L ~ 10 µm typical speeds v ~ 10^{5 }m.s^{1} viscosity h ~ 10^{3} Pa.s R ~ (10^{5})(10)(10^{6})(10^{3}) / 10^{3} ~ 10^{4 } ^{ } Flow is streamlined. 





REYNOLDS Number and energy dissipation Poiseuille's Law shows that viscosity is
responsible for loss of pressure  and hence is an energy dissipating
phenomenon. We are not talking about
energy loss due to turbulence, but about energy loss which occurs even when
the flow is streamlined. It comes
about through friction between the streamlines moving past one another. The criterion whether or not
much energy is lost in this way, is therefore whether or not there is much of
a velocity gradient throughout the whole of the liquid. Since most of this gradient occurs near a
boundary (in the so called Boundary
layer, it is the ratio of the size of the system to the size of the
boundary layer which is important. 





So now we can appreciate another reason why the Reynolds number is
important. Viscous effects can never
be neglected (i.e. the energy dissipated is appreciable) in low Reynolds
number situations: in thick liquids (h
large), or in small slow flow systems.
On the other hand viscous effects will not be important in thin
liquids or in large, fast flow systems.
(However in these latter systems remember that turbulence is always
possible, and energy can be lost through that means.) In general then, flow patterns will be different in systems with
low and with high Reynolds numbers.
In particular, in very low Reynolds number systems, the flow is
perfectly reversible since no
turbulent effects can occur anywhere. 


·
The method of swimming is quite different for Fishes (R ~ 10,000) and
spermatozoa (R ~ 0.0001). ·
Modes of boat propulsion which work in thin
liquids (water) will not work in thick liquids (glycerine). ·
It is possible to stir glycerine up, and then unstir it completely. You cannot do this with water. ·
If you were designing a circulatory system for
the human body, where a prime requirement is that as little energy as
possible should be dissipated, in order not to require the heart to pump any
harder than absolutely necessary, what Reynolds
number would you aim for? Compare this with the Reynolds number for
blood, which is somewhere between 1000 and 2000. 


Home activity Turn on a water tap
such that the flow is smooth and glassy.
This is streamline flow.
Increase the flow rate and observe as the flow becomes turbulent,
rough and ropey. See if you can
identify a flow where water leaves the tap in streamline flow but transits to
turbulent flow before hitting the sink.



