Pipe Flow Friction Factor Calculations

(1)

Workbook Contents

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Tab .

Tab . Contents (current tab)

Contents (current tab)

Tab !.

Tab !. Head oss!"rictional #ressure $rop

Head oss!"rictional #ressure $rop

Tab .

Tab . #ipe "low %ate

#ipe "low %ate

Tab #.

Tab #. %e&uired $iameter

%e&uired $iameter

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#ipe "low!"riction "actor Calculations +: (/.0. units)

for given flow rate, 1, pipe diam., $, pipe length, ,

2 in 3.4333 3.3334 ft 3.35627 533 ft 3.5628 3.233 cfs 8.5 5.69 53,4;4 3.33337;8

(Calculate f with the transition region e&uation and see if differs from the one calculated above.)

*ransition %egion "riction "actor, f: 3.3775

%epeat calc of f using new value of f: 3.3773

Calculation of Head oss, h

_

, and "rictional #ressure $rop,

∆

#

_f

,

pipe roughness,

ε

, and fluid properties,

ρ

<

µ

.

$nstructions

:

Enter values in blue boxes. Spreadsheet calculates values in yellow bo

.

%etermine &riction &actor, f, assuming completely turbulent flow '

f ( ).# * ! log

_+

%-$nputs

(enter values in the blue boes)

Calculations

(done by spreadsheet

#ipe $iameter,

%

_in = _{#ipe $iameter,}

_%

₌

#ipe %oughness, = "riction "actor,

f

=

#ipe ength,

0

= Cross-0ect.>rea,

1

=

#ipe "low %ate,

2

= >ve.?elocity,

3

=

"luid $ensity, slugs!ft8 _{%eynolds number,}

4e

₌

"luid ?iscosity, = _lb-sec!ft7

!.

Check on whether the given flow is "completely turbulent flow"

f ( '!5log

_+

)

f

=

f

=

ε

! =

-%6-.76*!.8-4e5f

-!

_669/

!

(3)

%epeat again if necessary: 3.3773 3.29 ft "rictional #ressure 93 psf "rictional #ressure 3.7 psi

f

=

.

Calculate h₀and :_f, using the final value for f calculated in step !

;<uations= h

₀

( f0-%63

!

_{-!g6 and :}

f

(

gh

0

"rictional Head oss,

h

₀ =

$rop,

:

_f =

(4)

@oody "riction "actor &uations

ft

#ipe %oughness ?alues

ft!sec

es

/

ft7

(5)

(6)

#ipe "low!"riction "actor Calculations ++: (/.0. units)

Calculations

9 in 3.8888 3.3334 ft 3.375;3 93 ft 3.3;8 3.6 ft 3.8 5.69 6.4 3.33337;8 774,768

*ransition %egion "riction "actor, f: 3.377;

%epeat calc of f using new value of f: 3.377;

%epeat again if necessary: 3.377;

Calculation of "luid "low %ate, 1, for given frictional head loss, h

_

, pipe

diam., $, pipe length, , pipe roughness,

ε

, and fluid properties,

ρ

<

µ

.

$nstructions

:

Enter values in blue boxes. Spreadsheet calculates values in yellow boxes

.

f ( ).# * ! log

_+

%-$nputs

(enter values in the blue boes)

#ipe $iameter,

%

_in = _{#ipe $iameter,}

_%

₌

#ipe %oughness, = "riction "actor,

f

=

#ipe ength,

0

= Cross-0ect.>rea,

1

=

>llowable Head oss,

h

₀ = _{>ssumed "low %ate,}

₂

₌

"luid $ensity, slugs!ft8 _{>ve. ?elocity,}

3

₌

"luid ?iscosity, = _lb-sec!ft7 _{%eynolds number,}

4e

₌

!.

f ( '!5log

_+

)

f

=

f

=

f

=

ε

! =

-%6-.76*!.8-4e5f

-!

_669/

!

(7)

9.2 ft!sec

3.93 cfs

AB: his is an iterative calculation, because an assumed value of 1 is used to start the

calculations. +f the final calculated value of 1 is different from the assumed value, then the

assumed value of 1 should be replaced with the calculated value of 1, leading to a new

calculated value for 1. *his should be repeated as many times as necessary to get the

calculated value for 1 to be the same as the assumed value. *his iteration typically converges

rather rapidly.

*his spreadsheet shows only the final assumed and calculated values of 1 (when they are e&u

+f the initial assumed value of 1 was 5.4 cfs, then subse&uent calculated and assumed values

for 1, leading to the final solution are as follows:

>ssumed 1, cfs

Calculated 1, cfs

5.4 3.4

3.4

3.8

.

Calculate 3 and 2, using the final value for f calculated in step ! in the %arcy Weisbach e<uatio

)3 ( !g5%5h

₀

-f506

-!

_{9 and 2 ( 3 %}

!

_-#6

"luid ?elocity,

3

=

(8)

@oody "riction "actor &uations

ft

cfs

#ipe %oughness ?alues

ft!sec ft7

(9)

l).

(10)

#ipe "low!"riction "actor Calculations +++: ( /.0. units )

Calculation of pipe diameter, $, for given flow rate, 1, pipe length, ,

(AB: his is an iterative calculation. >n initial assumed value of $ will be used.)

$nputs

Calculations

73 ft 9 in 3.3334 ft 3.8888 ft 533 ft 3.375;3 3.233 cfs 3.3;8 5.69 2.6 ft!sec 3.33337; 529,2;7

*ransistion %egion "riction "actor, f: 3.3783

%epeat calc of f using new value of f: 3.3783

pipe roughness,

ε

, head loss, h

_

, and fluid properties,

ρ

<

µ

.

$nstructions

:

Enter values in blue boxes. Spreadsheet calculates values in yellow boxes

.

f ( ).# * ! log

_+

%- >llowable Head oss,

h

₀ = >ssumed #ipe $iam,

%

_in =

#ipe %oughness, = #ipe $iameter,

%

=

#ipe ength,

0

= "riction"actor,

f

=

#ipe "low %ate,

2

= Cross-0ect.>rea,

1

= ft7

"luid $ensity, slugs!ft8 _{>ve. ?elocity,}

3

₌

"luid ?iscosity, = _lb-sec!ft7 _{%eynolds number,}

4e

₌

!.

) f ( '!5log

_+

)

f

=

f

=

ε

!

_/

=

-%6-.76*!.8-4e5f

-!

_669/

!

₉

(11)

%epeat again if necessary: 3.3783

3.394 ft = 5.3 in

AB*: *his iterative procedure doesnDt converge smoothly to a solution. +f the calculated pipe diameter in this step is larger than the assumed pipe diameter above, then replace the assumed pipe diameter value with the net larger standard pipe siEe. %epeat until you find the smallest standard pipe diameter that gives a smaller calculated re&uired pipe diameter. *hat is your solution.

'ith the eample values given here, an assumed pipe diameter of 8 inches gives a calculated pipe diameter re&uirement of 8.9 inches, increasing the assumed pipe diameter to the net standard pipe siEe ( 8.4 inches ) gives a calculated pipe diameter re&uirement of 5. inches, so a 8.4 inch siEe is the

minimum standard pipe diameter that will do the Fob.

0tandard nominal /.0. pipe siEes in inches:

5!, 5!9, 8!, 5!7, 8!9, 5, 5 5!9, 5 5!7, 7, 7 5!7, 8, 8 5!7, 9, 4, 2, , 53, 57, 59, 52, 5, 73, 79, 83, 97, 9, 49, 23

f

=

.

Calculate pipe diameter, % using the final value for f calculated in step !

) % ( f0-h

₀

63

!

_{-!g6 9}

(12)

@oody "riction "actor &uations

(13)