CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in...

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Transcript of CHE315 Pressure Drop and Friction Loss 2.10 Design Equations for Laminar and Turbulent Flow in...

CHE315 Pressure Drop and Friction Loss

Fanning friction factor f for friction loss in laminar flow

f is defined as drag force per wetted surface unit area (ts at the surface area) divided by the product of density times the velocity head (r v2/2):

22vf s

The drag force The wetted surface unit area 2Rp f LR 2

L

Dp

L

Rp

LR

Rp fffs

422

2

CHE315

CHE315

Example 2.10-

3

NOTE: If velocity and diameter are both unknown, Solution should be Trial –and-error soln. (or computerized).

Pressure Drop and Friction Loss

CHE315

Step by step procedure for trial-and error solution

1.Assume an initial value for the velocity (or the

diameter)

2.Calculate the Reynolds number (and e/D)

3.From the figure 3.10-3, read the corresponding

friction factor f

4.Substitute f into:

5.Compare the obtained value with the initial one

6.If values are different repeat from step2 with the

obtained value

24

2v

D

LfFf

Pressure Drop and Friction Loss

CHE315

Example 2.10-

4Example

2.10.5

Pressure Drop and Friction Loss

CHE315 Pressure Drop and Friction Loss

For gases, the equation 24

2v

D

Lfp f

can be rewritten as

follows:

avf D

LGfpp

2

4 2

21

vG

Pressure drop and friction factor in flow of gas

RT

MpRT

MpRT

M

mnRTpV

Ideal Gas Law:

CHE315 Pressure Drop and Friction Loss

DM

RTLGfpp

22

22

1

4

How did we arrive to this equation?

av

f D

LGfpp

2

4 2

21

RT

MpRT

MpRT

M

mnRTpV

Using Ideal Gas Law;

The following equation can be obtained

CHE315

Contraction

Friction

Expansion

Friction

kg

JvKh s

2

2

AL AS

vL vS

2

1

L

sex A

AK

L

sc A

AK 155.0

exhhchh

FittingsFriction 2

21vKh ff

Pressure Drop and Friction Loss

Kf :Turbulent: Table

2.10-1Laminar: Table

2.10-2

CHE315

22224

21

222 vK

vK

vK

v

D

LfF f

sc

sex

friction loss in Pipes SF

SkinFriction

Contraction

Friction

Expansion

Friction

FittingsFriction

24

2v

D

Lf

2

2s

ex

vK 2

21vK f

2

2s

c

vK

Pressure Drop and Friction Loss

CHE315

Example

2.10.6Example

2.10.7

Pressure Drop and Friction Loss

CHE315

FRICTION LOSSES IN NONCIRCULAR CONDUITS

The equivalent diameter D is defined as four times the hydraulic radius

rH, defined as the ratio of the cross-sectional area of the channel to the

wetted perimeter of the channel.:

channel ofperimeter wetted

channel of area sectionalcross4

HrD

Pressure Drop and Friction Loss