CIVE 2400 : Pipeflow - Lecture 1 09/04/2009

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CIVE2400: Pipeflow
-
Lecture 1
09/04/2009
1
School of Civil Engineering
FACULTY OF ENGINEERING
Fluid Flow in Pipes: Lecture 1
Dr Andrew Sleigh
Dr Ian Goodwill
CIVE2400: Fluid Mechanics
www.efm.leeds.ac.uk/CIVE/FluidsLevel2
Fluid Mechanics: Pipe Flow

Lecture 1
Fluid Flow in Pipes

Pressurised flow

Liquid or Gas

Above or below atmospheric
pressure

No free surface

That is “open channel flow”

“Real” viscous fluid

Interacts with boundary
Fluid Mechanics: Pipe Flow

Lecture 1
3
Resistance to flow

Flowing fluid

Shear stress where touches solid boundary

Both for pipes & open channels

Referred to as “frictional resistance”

Energy transfer between fluid and boundary

Experienced as a “loss” of energy in fluid

Energy “loss” at joints and junctions

Due to flow separation (a local friction
effect)
Fluid Mechanics: Pipe Flow

Lecture 1
4
This module:

Analysis of pipeline flow

How to quantify friction

What causes it

What is its magnitude

How significant it is

How to take account of friction

How to take account of other losses

Examples:

Pipes in series

Pipes in parallel

Branched pipes (small networks)
Fluid Mechanics: Pipe Flow

Lecture 1
5
Analysis of pipelines

Typical simple pipeline joining 2 reservoirs

Bernoulli
Constant

2
2
2
2
H
z
g
u
g
p
z
g
u
g
p
B
B
B
A
A
A
Fluid Mechanics: Pipe Flow

Lecture 1
6
Bernoulli Equation

Including losses
f
exit
L
L
entry
L
B
B
B
pump
A
A
A
h
h
h
h
z
g
u
g
p
h
z
g
u
g
p
expansion
2
2
2
2
Friction Loss
CIVE2400: Pipeflow
-
Lecture 1
09/04/2009
2
Fluid Mechanics: Pipe Flow

Lecture 1

p
A
= Atmospheric pressure

p
B
= Atmospheric pressure

u
A
= small (negligible)

u
B
= small (negligible)
f
exit
L
L
entry
L
B
B
B
pump
A
A
A
h
h
h
h
z
g
u
g
p
h
z
g
u
g
p
expansion
2
2
2
2
7
Bernoulli Equation (simplified)
f
exit
L
L
entry
L
pump
B
A
h
h
h
h
h
z
z
expansion
Fluid Mechanics: Pipe Flow

Lecture 1

Fluid flowing in pipe

Piezometer

Level rises
8
Pressure head
g
p
h
Pressure Head
Fluid Mechanics: Pipe Flow

Lecture 1

Fluid flowing in pipe

Piezometer &

L
-
shaped Piezometer

Levels rise
9
Velocity head
g
u
h
2
2
Velocity Head
g
u
g
p
2
2
g
p
Fluid Mechanics: Pipe Flow

Lecture 1
10
Shear stress on fluid

Newton’s law of viscosity

Shear stress proportional to velocity gradient

Viscosity,
, is the constant of proportionality
du
dy
du
dy
Fluid Mechanics: Pipe Flow

Lecture 1
11
Laminar and turbulent flow

Flow can be either

Laminar
-
low velocity

Turbulent

high velocity

(with a small transitional zone between)

Reynold' Number

Pipe flow nearly always turbulent
ud
ud
Re
Laminar flow:
Re < 2000
Transitional flow:
2000 < Re < 4000
Turbulent flow:
Re > 4000
Fluid Mechanics: Pipe Flow

Lecture 1
12
Reynolds Number Calculation

Pipe diameter:
0.5m

Crude oil:
Kinematic viscosity
= 0.0000232 m²/s

Water:
Dynamic viscosity µ = 8.90
10
−4
Pa∙s
What are the velocities when
Turbulent flow would be expected
to start?
CIVE2400: Pipeflow
-
Lecture 1
09/04/2009
3
Fluid Mechanics: Pipe Flow

Lecture 1
13
Reynolds Number Calculation

Crude oil:

Water:
ud
ud
Re
s
m
u
u
/
1784
.
0
10
23
.
2
5
.
0
4000
5
s
m
u
u
/
007
.
0
10


8.90
5
.
0
1000
4000
4
-
Fluid Mechanics: Pipe Flow

Lecture 1
14
Pressure loss due to friction in pipes

Cylinder of fluid:

Driving force (due to pressure)
Driving force = upstream force

downstream force
Driving force =
Direction of flow
w
w
Area A
Pressure p
Pressure p
-
p
P = F/A
pA
p
p
A
p
A
p
d
2
4
Fluid Mechanics: Pipe Flow

Lecture 1
15
Pressure loss due to friction in pipes

Retarding force (due to shear stress at wall)
Retarding force = shear stress x area acts
Retarding force =
Direction of flow
w
w
Area A
Pressure p
Pressure p
-
p
dL
w
w
=
wall
pipe

of

area
Fluid Mechanics: Pipe Flow

Lecture 1
16
Pressure loss due to friction in pipes
Driving force = Retarding force
pressure loss in terms of Shear Stress at wall
Direction of flow
w
w
Area A
Pressure p
Pressure p
-
p
p
d
dL
p
L
d
w
w
2
4
4
Fluid Mechanics: Pipe Flow

Lecture 1

Shear stress will
change with velocity

So shear stress
changes with Re

Laminar

Turbulent
17
Pressure loss velocity relationship
u
p
0
.
2
7
.
1
to
u
p
Fluid Mechanics: Pipe Flow

Lecture 1

This graph is empirical
Obtained from experiment

We would like to know
The relationship between
w
and Pressure

Will not get a general expression

But we will see a method of estimating
w
18
Pressure loss shear stress relationship
CIVE2400: Pipeflow
-
Lecture 1
09/04/2009
4
19
Today’s lecture:

Fluid flow in pipes

Analysis of pipelines

Bernoulli Equation (revision)

Pressure loss / Wall Shear Stress and
velocity relationship