ecw321-ecw301-topic 1 (part 2).pdf

Topic 1(Part 2):

Pipe flow analyses

Overview

UiTMKS2/BCBIDAUN/ECW301/ECW321

1.1Steady flow in pipes

1.1.1 Laminar flow in

circular pipes under steady

and uniform conditions

1.1.2Turbulent flow in

bounded conduits under

steady and uniform

conditions

1.1.3 Moody Chart

1.1.4 Pipe problems

1.1.5 Separation losses

1.1.6 Equivalent length

1.2 Analysis of steady flow in

pipelines

1.2.1 Energy equation in pipe

flow

1.2.2 Flow through pipes in

series


parallel


branching pipes

1.2.5 Quantity Balance Method

Learning Outcomes


By the end of this lesson, students should be able to:

Discuss Chezy Equation and its application (CO1-PO1)

Able to apply Darcy Weisbach Equation to solve turbulent

flow problems (CO1 PO3)

Douglas Chapter 10.3 & 10.5


1.1.2Turbulent flow in bounded conduits

under steady and uniform conditions


Most civil engineering application, the flow is turbulent in

nature.

An expression for head loss due to friction in conduit

under steady and uniform flow for turbulent condition

will be derived.

This expression is applicable for both closed and open

conduit.


Consider the fluid element within a conduit.


Forces acting:

Forces due to static pressure at both ends : p1, p2

Forces due to shear stress opposing the wall acting along the

conduit wall:

Weight of the element acting downwards: W


Summing the forces along the pipe axis:

Substituting,

Therefore,

Dividing through by AL and rearranging the equation,

0sin21 WLPApAp

L

zgALW

sin,

021 zgALPApp

01 21 A

Pzgpp

L


Simplifying by substituting the first term with which

is the piezometric pressure loss over the distance L,

Introducing the hydraulic mean depth m, ratio of flow

area A divided by wetted perimeter P,

Substituting,

dx

dp*

0*

A

P

dx

dp

P

Am

dx

dpm

mdx

dp

*

*

0


The shear stress is a function of the type of surface that

the wall of the conduit is made of.

The stress is dependent on the resistance offered by the

surface of the wall of the conduit and measured by

dimensionless friction factor f.

It is a measure of the roughness of the surface and given

as,

Rewriting previous equation,

2

2vf

m

vf

dx

dp

dx

dpm

vf

2

22*

*2


Let frictional head loss over the length be,

Substituting dx with L,

g

dph f

*

m

vf

L

gh

L

dp f

2

2*


Rearranging the equation,

gm

fLvh f

2

2

perimeter wetted

flow of area sectional cross

depthmean hydraulic

onaccelerati nalgravitatio

velocityaverage

occurs loss head over whichconduit oflength

factorfriction flow

Llength over loss head frictional

P

A

P

Am

g

v

L

f

h f

Applicable for both open and closed conduits


Rearranging previous equation,

Where ,

gm

fv

L

h f

2

2

gradient hydraulic iL

h f

mif

gv

mif

gv

gm

fvi

2

2

2

2

2


Letting Cf

g

2

conduit in the velocity average

depthmean hydraulic

gradient hydraulic

surface of typeon thedependent ist which coefficienChezy

v

m

i

C

miCv Chezy formula, usually

applicable for open channel

but can also be applied for closed

conduit


Consider turbulent flow in circular pipes running full,

g

v

d

fL

gd

fLvh

d

d

d

P

Am

f2

4

42

4

4

22

2

g

v

d

fLh f

2

4 2

Darcy-Weisbach equation for head

loss in

circular pipes


Sometimes it is convenient

to write Darcy equation in

terms of Q when flowrate

is known and velocity is not.

The answer differs by only

1% but still acceptable.

5

2

5

2

52

2

22

3

03.3

32

4

4

d

fLQh

d

fLQh

gd

fLQh

d

Q

d

Q

A

Qv

f

f

f

End of Part 2

Part 3: Douglas Chapter 10.4


ecw321-ecw301-topic 1 (part 2).pdf

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