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VE2400: Pipeflow - Lecture 2 09/04/200
School of Civil EngineeringFACULTY OF ENGINEERING
Fluid Flow in Pipes: Lecture 2
Dr Andrew Sleigh
Dr Ian Goodwill
CIVE2400: Fluid Mechanics
www.efm.leeds.ac.uk/CIVE/FluidsLevel2Fluid Mechanics: Pipe Flow
Lecture 2
Laminar
Turbulent
tw is almost impossible to measure
2
Pressure loss velocity relationship
Fluid Mechanics: Pipe Flow Lecture 2 3
Pressure loss in Laminar Flow
In laminar flow it is possible to do theoretical
analysis
fluid particles move in straight lines
Hagen-Poiseuille equation
See level 1 fluids notes
In terms of head loss
2
32
d
Lup
2
32
gd
Luhf
ghp
Fluid Mechanics: Pipe Flow Lecture 2
Laminar flow example
Determine the diameter of a pipe that is to convey 0.057
cumecs(m3/s) of oil a horizontal distance of 300m, if the pressure
loss is not
to be greater than 140 kN/m2.
At the operating temperature the relative density of the oil is
0.9 and
the dynamic viscosity is 1.43 Ns/m2.
Flow velocity
Hagen-Poiseuille
Equate
Check Re:
2
32
d
Lup
222
198.1030043.132
1000140
32d
d
L
pdu
222
0726.0
142.3
4057.0
4/ ddd
Qu
md
dd
29.0
198.100726.0 2
2
86.00726.0
2
du
157
43.1
29.086.010009.0Re
ud
7/26/2019 Lecture02 Pipeflow Handout
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VE2400: Pipeflow - Lecture 2 09/04/200
Fluid Mechanics: Pipe Flow Lecture 2 7
Introduction of Friction factor
To make use of this equation we must introduce
afriction factor, f
Equating and rearranging gives
For a circular pipe,
Giving
2
2uf
tL
ghm
f
t
gm
fLuhf
2
2
4
4/2 d
d
d
P
Am
gd
fLuhf
2
4 2
Fluid Mechanics: Pipe Flow Lecture 2 8
Darcy-Weisbach equation
This is the Darcy-Weisbach equation
Gives head loss due to friction in a circular pipe
Often referred to as the Darcy equation
In terms of Q
In metric terms, g=9.81m2/s then
Or
ud
AuQ4
2
gd
fLuhf 2
4 2
2
4
d
Qu
5
2
2
64
dg
fLQhf
5
2
03.3 d
fLQhf
5
2
3d
fLQhf
Fluid Mechanics: Pipe Flow Lecture 2 9
Darcy-Weisbach equation
Have an equation to describe head-loss due to
friction
In terms of velocity u
Of discharge Q
And a friction factor, f
The value of fis crucial to calculation of hf
How do we find this?
gd
fLuhf
2
4 2
5
2
3d
fLQhf
Fluid Mechanics: Pipe Flow Lecture 2 10
f, American fand
The fdescribed here is that common in UK
(in text books and practice)
In US (and some text book) fameri can
= 4f,
so
To try and avoid confusion this is sometime
written as ,
BE CAREFULL!
When using any book, look at the equation for hf
gd
fLuhf
2
4 2
5
2
3d
LQ
hfl
gd
fLuhf
2
2
Fluid Mechanics: Pipe Flow Lecture 2 11
Pipeline Analysis
Two reservoirs have a height diff erence 15m.
They are connected by a pipeline 350 mm in diameter and 1000 m
long with a friction
factor fof 0.005. What is the flow in the pipe? (ignore all
local losses)
fexitLLentryLpumpBA hhhhhzz expansion
15m
L=1000m
f =0.005
d=0.35m
slitressmQ
QQ
d
fLQ
/217/217.00473.0
33.31735.03
1000005.0
315
3
2
5
2
5
2
Fluid Mechanics: Pipe Flow Lecture 2 12
What is f dependent on?
The friction factor depends on many physical things
hf
L
hfv2
hf1/d
hfdepends on surface roughness of pipes,
k = size, k spacing, a = shape of particles
hfdepends on fluid density and viscosity
hf independent of pressure difference in pipe
Cannot be constant!
Can be written:
a
,
',,d
k
d
kudf
fis complex !!
