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D V ρρρρ====Reynolds numb

De

r

V Re

ρρρρ====

µµµµ

� For laminar flows, the expression for friction factor is,

; Re16

f 0021==== ≤≤≤≤

� For turbulent flows, curves have been constructed using

; Re16

f R

00e

21==== ≤≤≤≤

� For turbulent flows, curves have been constructed using

experimental data. These curves have been fitted into

equations. These are (for hydraulically smooth pipes),equations. These are (for hydraulically smooth pipes),

0.079f

0.25Re

; ( formula)5

2100 Re 10 Blasius==== < ≤< ≤< ≤< ≤

(((( ))))

(((( ))))

Re

1 4.0 log Re f 0.4

10f; ( formula)

6230 Pran0 Re 4 10 dtl= −= −= −= − < ≤ ×< ≤ ×< ≤ ×< ≤ ×

(((( ))))(((( )))) (((( ))))

2f

3 / 2e 3 5

; where ;2 1 2

2

+ α+ α+ α+ αΨ =Ψ =Ψ =Ψ =

αααα α αα αα αα α====

+ ++ ++ ++ +αααα(((( )))) (((( ))))2

63 Barenbl

1 2

3 and ; ( 070 Re 3.2

1

tt10 a3

α αα αα αα α

< ≤< ≤< ≤< ≤

α +α +α +α + ΨΨΨΨ

+ ++ ++ ++ +

α =α =α =α = ××××

αααα

formula)6

3 Barenbl and ; ( 2 ln Re

070 Re 3.2 tt10 a3< ≤< ≤< ≤< ≤α =α =α =α = ×××× formula)

0.2f 0.046 Re ;

5 65 10 Re 10

−−−−==== × <× <× <× < ≤≤≤≤

0.125f 0.0014 +

63000 Re 3;

0. 2R

03

e1<<<< ≤ ×≤ ×≤ ×≤ ×====

Re

� For turbulent flows (rough pipes), an empirical relation is

given as,

; ( equation)

101 6.9 k D 9

3.6 log 0.4 Haaland

= − + −= − + −= − + −= − + − ; ( equation)

1 6.9 k D 9 3.6 log 0.4

10 Re 3.7fHaaland

= − + −= − + −= − + −= − + −

k4 6

4 1

protuberance (signfies roughne

and

where k = height

0

R

o

e 4 10 0 0

ss

. 5

)f

0D

×××× ××××< ≤ << ≤ << ≤ << ≤ < <<<<

protuberance (signfies roughnewhere k = height o ss)f

PIPE FITTI2GSPIPE FITTI2GS

450 elbow 900 elbow 900

square elbow

wheelwheel

gland

spindle

bonnetgland

packing

bonnet

bodybody

disk

Dh DD

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