FRICTION FACTOR

• A common parameter used in LAMINAR and especially in TURBULENT flow is the Fanning friction factor, f

• ‘f ’is as the ratio defined of wall shear stress to the product of the density and the velocity head

22vf

We know that, for flow of fluid in a circular tube,

Sub. the above eqn in the previous one…

For laminar flow,

by comparing above two equations,….

2

4 DPDL

LvPDf 22

2

32

D

vLP

Dvf

16

Re

16

Nf

For LAMINAR flow

General Eqn for “f”

F.L in B.Eqn• In a straight pipe…..the friction losses to be used

in B.Eqn is…..• We know,

• But all the terms in B.Eqn are having the units of J/kg…..so friction losses is written by modifying the above eqn as…

LvPDf 22

2v

DL

4fh2

f

P

lossesfriction

2v

DL

4f2

22

22b

bb

Pa

aa v

gZp

Wv

gZp

• In turbulent flow, it is not possible to predict the value of ‘f ’ theoretically

• It should be determined empirically (experimentally)

• It also depends on surface roughness of the pipe.

• To predict the value ‘f ’ …. Friction factor chart (MOODY chart) is available

FRICTION FACTOR---TURBULENT FLOW

‘f’ vs NRe

Friction factor chart (MOODY chart)

• Relative roughness factors ε/D where ‘ε’ is the roughness parameter, represents the average ht in ‘m’ for projections from the wall

• For commercial steel pipe, ε = 4.6 x 10-5m

Prob 1

• Water flows in a smooth plastic pipe of 200mm dia @ a rate of 0.1m3/s. Det the friction factor for this flow:

• Re = 6.36x105------Turbulent flow

• For smooth pipe, ε/D = 0

• From Moody’s chart…..

• f = 0.003

Prob 2

• Calculate the press. drop along 170m of 5cm dia, horizontal steel pipe thro which olive oil at 20ºC is flowing at a rate of 0.1m3/min. density 910kg/m3 & viscosity 84x10-3 Ns/m2

• We know,

• NRe = 460

• For Laminar flow, f = (16/NRe )= 0.0347

• ∆P=154.709kPa

LvPDf 22

Prob 3• Water is to flow thro 300m of horizontal pipe at a

rate of 0.06 m3/s. A head of 6m is available. What must be the pipe dia? Take f = 0.0056

• We know, • v =(Q/A)= 0.0764/D2

• and ∆P = hg• D = 0.201cm

ghD

vLfP

fLv

PD

2

2

2

2