Open Channel VS Pipe Flow

a report about the comparison between the different characteristics of the open channel and the pipe flow presented to Dr. Hala Mahmoud Ragaei

1. Pipe flow vs Open Channel

To : Doctor Engineer Hala Mahmoud Ragaei
From : Group 11
ماصع اللهدبع– دشار دمحأ– لداع ةريمأ– لداع ناميإ– زياف دمحأ– لامج ماهير– دمحم ةورم-
دمحم ميهاربإ– ملاسلادبع ءامسأ– دمحم ءامسأ– يسنم ءامسأ – دومحم ةمطاف

2. Open Channel Pipe Flow
The water flows without filling the pipe or the flow has a
free surface .

The pipe is completely filled with the fluid being
transported ( no free surface of flow ) .


Pressure at the free surface remains constant with value of
atmospheric pressure
Pressure in the pipe is not constant
The main drivig force is Gravity (potential work)
Water flows from the upstream (the high energy head)
towards the down stream (the lower energy head ) by the
power of gravity.
The main driving force is (Pressure work ) Pressure
gradient along the pipe .
Flow cross sectional area may change throughout the
length depending on the depth of the flow , it can be
rectangular ,trapezoidal ,triangular ,parabola & circular
Kinds of Open Channel:
Canal, Flume, Chute, Drop, Culvert, and Open-Flow
Tunnel.



Flow cross sectional area remains constant and it is equal
to the cross sectional area of the pipe ( conduit )
which is usually circular.

4. Changes in velocity profile as the size of the close-packed
granular roughness increases relative to flow depth.


Changes in flow structure as roughness spacing decreases
relative to roughness height.

The internal roughness of a pipe is an important factor
when considering the friction losses of a fluid moving
through the pipe.

Relative roughness



The relative roughness of a pipe is its roughness divided
by its internal diameter or e/D, and this value is used in the
calculation of the pipe friction factor, which is then used
in the Darcy-Weisbach equation to calculate the friction
loss in a pipe for a flowing fluid.
Absolute Roughness (ε)
The roughness of a pipe is normally specified in either
mm or inches and common values range from 0.0015 mm
for PVC pipes through to 3.0 mm for rough concrete
pipes.Absolute roughness is a measure of the surface
roughness of a material which a fluid may flow over.
Absolute roughness is important when calculating

5. pressure drop particularly in the turbulent flow regime.

Characteristics flow parameters : Flow depth deduced
simultaneously from solving both continuity and
momentum equation
Characteristics flow parameters : velocity deduced from
continuity

Maximum velocity occurs at a little distance below the
water surface . The shape of velocity profile depends on
the channel roughness .

The velocity distribution is symmetrical about the pipe
axis . Maximum velocity occurs at the pipe center and
velocity at pipe walls reduced to zero .

6. Laminar and Turbulency in open channel
The behavior of flow in rivers and open channels is
governed primarily by the effects of gravity and fluid
viscosity relative to inertial forces. Effects of surface
tension are usually negligible for natural rivers.
In laminar flow, parcels of fluid appear to travel in
smooth parallel paths. Laminar flow occurs very rarely in
natural open channels. When the surface of a river
appears smooth or glassy, it does not necessarily mean
that the flow is laminar; rather, it is most likely tranquil,
though turbulent flow
In turbulent flow, pulsatory cross-current velocity
fluctuations cause individual parcels of fluid to move in
irregular patterns, while the overall flow moves
downstream.
One effect of the microstructure of turbulent flow is the
formation of a more uniform velocity distribution.




Laminar and Turbulency in pipe flow
When the fluid is moving slowest, get a well-defined
streak-line. This flow situation is called laminar flow.

When the fluid is moving faster, get an irregular streak-
line which blurs and spreads the dye out. The streak-line
also fluctuates randomly with time. This is called
turbulent flow.

When the fluid is moving at an intermediate velocity,
there are irregularities in the streak-line, but the streak-
line is still well defined. This is called transitional flow

7. Classification of flow in open channel ( States Of Flow )
ange with time: When discharge doesn't ch Steady Flow
’t change for a selected lengh fo section of the channeln: when depth of fluid doesniform flowU
’t change with time and depth remain constant for a selected sectionn:when discharge does niform steady flowU
to as a prismatic channel edrrefer –cross section should remain unchanged -
: when depth changed but discharge remain the same varied steady flow
ong channel length of interest.: when both depth and discharge change al varied unsteady flow
: depth change is rapid flow rapidly varing
: depth change is gradual . gradually varing flow

Section 1 – rapidly varying flow
Section 2 – gradually varying flow
Section 5 – gradually varying

8. Reynolds number for channel flow :
NR = vR/υ
Where R is the hydraulic radius ( metric units )
For channel flow
NR < 500 – laminar
NR > 2000 – turbulent
Reynolds number for pipe flow :
NR = vD/υ
where v is the mean velocity , D is the diameter of pipe ,
and υ is the kynematic viscosity of fluid
For pipe flow
NR < 2000 – laminar
NR > 4000 – turbulent
. Liquid surface itself represents the hydraulic grade line
(HGL) , which is referred to as the zero pressure
reference
. The energy gradient line (EGL) is at a distance equal to
the velocity head above the hydraulic gradient
. For uniform flow in an open channel, the drop in the
energy gradient line is equal to the drop in the bed.


. Line joining piezometric surface (Z+p/ ɣ) indicates the
hydraulic Grade line (HGL) , which is the sum. Of the
elevation and the pressure head
. The energy gradient line (EGL) is at a distance equal to
the velocity head above the hydraulic gradient
. There is no relation between the drop of the energy
gradient line and slope of the pipe axis.

9. In both open and pipe flow the fall of the energy gradient for a given length of channel or pipe ( hL) represents the
loss of energy by friction . When considered together, the hydraulic gradient and the energy gradient reflect not only
the loss of energy by friction, but also the conversions between potential and kinetic energy.

Proving Bernoulli's Equation for Pipe flow and Open channel
The energy calculated at one location in the flow will be equal to the energy calculated at any other location in the
same flow



The energy for the flow will have a potential energy component calculated from the depth of water in the flow, a
pressure component, and a kinetic energy component calculated from the velocity of the flow moving through the
:Bernoulli equationh the channel. This is depicted throug

E = energy [=] Length,
v = velocity [=] Length/Time,
g = acceleration due to gravity [=] Length/Time2,
y = depth of water in the flow [=] Length,
p = pressure [=] Force/Length2, and
= specific gravity of the fluid [=] Force/Length3
For two locations in the system with the datum chosen as the bottom of a channel with no slope:


For an open channel flow the fluid, water, is open to the atmosphere so that the pressure throughout the system can be
(2)
(3)

10. considered equal to atmospheric pressure. Therefore, the pressure term will be the same (hydrostatic) at all points in
the system, reducing the equation to:

(4)

. The streamlines of the flow are parallel.
. the elevation of the surface streamline is z + y. The gauge pressure here is ( zero ) , so Bernoulli's Equation for this
streamline is ( z + y + V
2
/2g = C )
. Now for the bottom streamline, the gauge pressure is (γy) , so that p/γ = y, and Bernoulli's equation is z + y + V
2
=
C, where C has the same value as for the top streamline.
. At any intermediate height y',
(z + y' + γ(y - y')/γ + V
2
/2g = C).
Therefore, C, the energy per unit weight, has the same value at any depth. The part y + V
2
/2g is the specific energy E,
and is the energy per unit weight referred to the stream bed.

For a rectangular channel the flow velocity can be related to a discharge rate per unit width, q, such that:



And
(5)
(6)

11. For given values of unit discharge, q, a specific energy diagram depicting energy and the depth of water, y, can be
developed. The specific energy is the energy above the datum, which we have chosen as the bottom of the channel.

(7)

12. the Reynolds number (Re) is a dimensionless quantity that is used to help predict similar flow patterns in different
fluid flow situations. The concept was introduced by George Gabriel Stokes in 1851, but the Reynolds number is
named after Osborne Reynolds (1842–1912), who popularized its use in 1883.
The Reynolds number is defined as the ratio of momentum forces to viscous forces and consequently quantifies the
relative importance of these two types of forces for given flow conditions. Reynolds numbers frequently arise when
performing scaling of fluid dynamics problems, and as such can be used to determine dynamic similitude between two
different cases of fluid flow. They are also used to characterize different flow regimes within a similar fluid, such as
laminar or turbulent flow:
 laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by
smooth, constant fluid motion;
 turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce
chaotic eddies, vortices and other flow instabilities.
The Reynolds number is defined below for each case.

where:
 is the maximum velocity of the object relative to the fluid (SI units: m/s)
 is a characteristic linear dimension, (travelled length of the fluid; hydraulic diameter when dealing with river
systems) (m)
 is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))

13.  is the kinematic viscosity ( ) (m²/s)
 is the density of the fluid (kg/m³).
Note that multiplying the Reynolds number by yields , which is the ratio of the inertial forces to the viscous
forces. It could also be considered the ratio of the total momentum transfer to the molecular momentum transfer.
For flow in a pipe or tube, the Reynolds number is generally defined as:

where:
 is the hydraulic diameter of the pipe; its characteristic travelled length, , (m).
 is the volumetric flow rate (m3/s).
 is the pipe cross-sectional area (m²).
 is the mean velocity of the fluid (SI units: m/s).
 is the dynamic viscosity of the fluid (Pa·s = N·s/m² = kg/(m·s)).
 is the kinematic viscosity ( (m²/s).
 is the density of the fluid (kg/m³).
For shapes such as squares, rectangular or annular ducts where the height and width are comparable, the
characteristical dimension for internal flow situations is taken to be the hydraulic diameter, , defined as:

where A is the cross-sectional area and P is the wetted perimeter. The wetted perimeter for a channel is the total

14. perimeter of all channel walls that are in contact with the flow. This means the length of the channel exposed to air is
not included in the wetted perimeter.
For a circular pipe, the hydraulic diameter is exactly equal to the inside pipe diameter, . That is,

For an annular duct, such as the outer channel in a tube-in-tube heat exchanger, the hydraulic diameter can be shown
algebraically to reduce to

where
is the inside diameter of the outside pipe, and
is the outside diameter of the inside pipe.

The behavior of open channel flow is governed by the effects of viscosity and gravity relative to the inertial forces of
the flow. Surface tension has a minor contribution, but does not play a significant enough role in most circumstances
to be a governing factor. Depending on the effect of viscosity relative to inertia, as represented by the Reynolds
number, the flow can be either laminar, turbulent, or transitional.

For flow of liquid with a free surface, the hydraulic radius must be determined. This is the cross-sectional area of the
channel divided by the wetted perimeter. For a semi-circular channel, it is half the radius. For a rectangular channel,
the hydraulic radius is the cross-sectional area divided by the wetted perimeter. Some texts then use a characteristic
dimension that is four times the hydraulic radius, chosen because it gives the same value of Re for the onset of
turbulence as in pipe flow, while others use the hydraulic radius as the characteristic length-scale with consequently
different values of Re for transition and turbulent flow.

15. The loss of energy calculated by
Chezy formula :












V:mean velocity




factor is called chezy constant



:hydraulic radius




: the loss of head per unit length

And Bernoulli equation:
























The loss of energy is classified as follows :
Major energy losses :
This loss due to the friction calculated by
Darcy formula:





:the loss of head due to friction
:coefficient of friction
: length of pipe
V :mean velocity
D: diameter of pipe

and chezy formula











V:mean velocity




factor is called chezy constant



:hydraulic radius




: the loss of head per unit length

16. Minor energy losses:
These losses due to:
Sudden enlargement ( expansion ) of pipe
Sudden contraction of pipe
An obstruction in pipe
Bend in pipe
Pipe fitting ( such as valves and elbows )

17. Application of Bernoilli's Equation on Open Channel

Application of Bernoilli's Equation on pipe flow

18. Examples of Design

Examples of Design

19. Sources
http://udel.edu/~inamdar/EGTE215/Laminar_turbulent.pdf
https://en.wikipedia.org/wiki/Hydraulic_head
http://www.cs.cdu.edu.au/homepages/jmitroy/eng247/sect09.pdf
-to-introduction-090-sciences/12-planetary-and-atmospheric-http://ocw.mit.edu/courses/earth
-fall-structures-sedimentary-generated-current-and-transport-sediment-motions-fluid
textbook/ch4.pdf-2006/course
http://www.tvrl.lth.se/fileadmin/tvrl/files/vvr090/lecture7_open_channel.pdf
http://www.aerodrag.com/Articles/ReynoldsNumber.htm
www.nptel.ac.in/courses/105106114/pdfs/.../2_29.pdf
Wikipedia, the free encyclopedia -Bernoulli&apos;s principle
https://en.wikipedia.org/wiki/Dimensionless_quantity
https://en.wikipedia.org/wiki/Dimensionless_Specific_Energy_Diagrams_for_Open_Channel_Flow
n.wikipedia.org/wiki/Fluid_dynamicshttps://e
channel_flow-https://en.wikipedia.org/wiki/Open

20. https://en.wikipedia.org/wiki/Pipe_flow
https://en.wikipedia.org/wiki/Fluid_dynamics
https://en.wikipedia.org/wiki/Hydraulic_head
http://iitg.vlab.co.in/?sub=62&brch=176&sim=1635&cnt=1
http://pubs.usgs.gov/of/1988/0707/report.pdf
https://attachment.fbsbx.com/file_download.php?id=135454603483819&eid=ASt9TymdrdzmC
-pkLdTgXZaPIY9J_8ha6bK7hspUSUv6WKvnzhuCBVBauBMyc8
ZpyzrA_jtA-wZ9Ks&inline=1&ext=1447966292&hash=ASvci

( some of the sources )