REYNOLDS NUMBER ENERGY LOSSES DUE TO FRICTION (Topic 4).ppt

8/10/2019 REYNOLDS NUMBER ENERGY LOSSES DUE TO FRICTION (Topic 4).ppt

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LEARNING OUTCOMES

Upon completion of this course, students should beable to:

Explain clearly the basic principles andcharacteristics of fluid mechanics, and fluid flows inpipe and open channel (C3)

www.themegallery.com

( PLO1;CLO1;LD1;C3 )


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4.1 Understand the behaviour of fluidsflowing in pipes

4.1.1 Define steady flow and unsteady flow

4.1.2 Explain laminar flow, turbulent flow and

transition flow

4.1.3 State the Reynolds number formula

4.1.4 Identify the limiting values of the Reynolds number

4.1.5 Calculate the Reynolds number



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Type of Flow

i- Laminar flow.

- Laminar flow is when the particles of fluidmoving in straight lines.

- Low velocity which call streamline Fluid particle path

in the pipe

Diagram

4.1

ii- Transition flow.

When the flow changes from laminar flow to turbulent

flow conditions,


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iii- Turbulent flow

The particles is bent and curved lines that cross each

other.

iv. Uniform flow

Uniform flow is when the velocity of the fluid andparticles in the pipe section is the same at all side.

V1=V2

V V1


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V- Non-Uniform flow

VV1

Nota:-

V V1

Non-uniform flow is the velocity of fluid particles is different from

one section to another.

The steady flow is the flow which have a flowrate

(volume flow per second) which is the same throughout the pipe

iv- Steady flow

VV1

V V1

Nota:-

Q1 = Q2

A1V1 = A2V2

vi- Non-Steady flow

Irregular flow / non steady flow is the flow which have a flowrate

(volume flow per second) is not the same throughout the pipe.


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To State and Use of Reynolds NumberFormula

Re =

Vd

or Re = v d

Reynolds fou nd for ;

Re


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Reynolds number

Experimental Reynolds

- The experiment is designed to see how the flowing ina pipe, ie whether it is laminar, turbulent orintermediate.

- This experiment was

initiated by the :

Prof. Osborne Reynold

- Prof. Osborne conclude that

flow condition be affected by

dynamic viscosity, density, diameter & velocity


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Example 1

Fluid flow in a pipe diameter of 30 cm with a

velocity of 0.21m/s and the kinematicviscosity 1.14mm2/s, calculate the Reynoldsnumber and specify the type of flow

vd6

1014.1

30.021.0

x

x

Re ==

= 55263

It is a turbulent flow because, Re > 2000.


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4.2.1 Explain main losses and minor losses in a pipe system

4.2.2 Define the friction factor

4.2.3 Explain Darcys equation for computing the energy

loss due to friction for either laminar or turbulent flow

4.2.4 Explain the Hagen-Poiseuille equation for

computing the energy loss due to friction in laminar flow

4.2.5 Determine the friction factor using Moodys Diagram

4.2.6 Determine the energy loss due to friction



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Contents

2 types of losses in a pipe system1

Darcy-Weisbach formula2

Places where minor head losses may

possibly occur (entry & exit area, suddenly

enlargement, suddenly reduction, bend and

valve

3

Flow rate in pipe system4


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HEAD LOSS

MAIN LOSSES- Darcy-Weisbach

formula

- Hf= 4fLV

2

2gd

= fLQ2

3d5

2 TYPES OF HEAD LOSS

MINOR LOSSES

- Entrance loss- Exit loss

- Suddenlyenlargement- Suddenly

Contraction- Bend- Valve


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FORMULA

MAIN LOSSES:

-Energy losses due to friction in pipe system

- Darcy-Weisbach formula

Hf= 4fLV2

2gd

@ = fLQ2

3d5

f = friction coefficient l = pipe length (m)

v = velocity (m/s)

d = pipe diameter (m)

Q = flowrate (m3/s)


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EXAMPLE 1

Calculate the head loss (energy) due to friction in the

pipe 500 m long and 20 cm diameter when water flowwith a velocity of 3m/s. Take f (coefficient of friction) =0.01.

Given: length of pipe (l) = 500 m

Diameter (d) = 20 cmVelocity (v) = 3 m/s

Friction coeff(f) = 0.01

Used formula hf=hf = 4 ( 0.01) ( 500) ( 3 )2

2 x 9.81 (0.2)

= 45.87 m


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EXAMPLE 2

Calculate the head loss (energy) as the

resistance to friction in the pipe 300 m longand 150 mm diameter when the flow rate is2.75m3/min. (f = 0.01 )

Length of pipe = 300 m

Diameter = 150 mmFlowrate = 2.75 m3/ min


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EXAMPLE 3

Calculate the head loss (energy) as the resistance to friction inthe pipe 300 m long and 150 mm diameter when the flow rateis 2.75m3/min. (f = 0.01 )

Length of pipe = 300 mDiameter = 150 mmFlowrate = 2.75 m3/ min

Used formula hf = Q = 2.75 m3/min

Change into m3/sQ = 2.75 m3/60 s= 0.046 m3/s

From formula flowrate Q = AVV = Q/A

= 0.046( 0.15)2/4

= 2.6 m/s.

hf= 4 (0.01)(300 )(2.6 )2

2(9.81)(0.15)

= 27.56 m

gd

vlf

2

...4 2


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EXAMPLE 4

Head difference between the two end pipesof 300mm diameter, 250m long and is 1.5m.

calculate the flow rate through the pipe ifthe coefficient of friction is 0.01.

Given: a head difference (hf) = 1.5 m

The pipe length = 250mDiameter = 0.3 m

Solution :

hf=

1.5 = 0.01( 250 ) Q2

3 ( 0.3 )5

Q = 0.0661 m3/s

5

2

3

..

d

Qlf


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EXAMPLE 5

A tank was built four miles of a student

dormitory that can accommodate 5000students. Water delivered from the tank tothe hostel with a pipe. Every student in adormitory with 200 liters per day. Water ispumped to the hostel for 20 hours a day. If

the head losses due to friction is 20m ofwater and the pipe friction coefficient is0.008, calculate the diameter of the pipeused.

Given: a head difference (hf) = 20 mThe pipe length = 200 mThe coefficient of friction = 0.008


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hf = fl Q2

3d5

20 = 0.008(4000)(0.01389)

3 (d )5

d =

Kadaralir Q = 5000x200

= 1 x 106liter

=

= 0.01389m3/s606020

10101 36

xjamx

xx


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4.2.4 Explain the Hagen-Poiseuille equationfor computing the energy loss due to

friction in laminar flow

Hagen-Poiseuille equation defines the flowthrough a tube and how this flow is affected bythe attributes of the tube, the length and radius,and the attributes of the fluid and also theviscosity.

The Hagen-Poiseuille formula

hf= 32 Lvgd2

Where, -Dynamic viscosity d - diameterL - length of pipe

v - velocity

g- acc. of gravity


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4.2.5 Determine the friction factor usingMoodys Diagram


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A Moody Diagram can be used to estimatefriction coefficients

The Moody friction factor - (or f)- is used inthe Darcy-Weisbach major loss equation. Thecoefficient can be estimated with the diagram

above.

If the flow is transition - 2300 < Re < 4000- theflow varies between laminar and turbulent flow

and the friction coefficient is not possible todetermine. The friction factor can usually beinterpolated between the laminar value atRe =2300 and the turbulent value at Re = 4000.


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http://www.engineeringtoolbox.com/docs/documents/618/pipefric.pdfhttp://www.engineeringtoolbox.com/docs/documents/618/pipefric.pdf


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EXAMPLE 1

Water with a dynamic viscosity 1.49x10-3 Ns/m2 flows

through a pipe of 0.3 cm in diameter with a velocity of0.9m/s. The length of the pipe is 9m. Given f =16/Re

a) Calculate the Reynolds number and state the type offlow

b) Calculate the head loss due to friction, using Hagen-Poisulle formula

c) Calculate the head loss due to friction, using Darcy-Weisbach formula


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REYNOLDS NUMBER ENERGY LOSSES DUE TO FRICTION (Topic 4).ppt