1. 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

2. 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,….
General Eqn for “f”
For LAMINAR flow

3. 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…

4. FRICTION FACTOR---TURBULENT FLOW
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
‘f’ vs NRe

5. Friction factor chart (MOODY chart)

6. 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

7. Prob 1
Water flows in a smooth plastic pipe of 200mm a rate of 0.1m3/s. Det the friction factor for this flow:
Re = 6.36x Turbulent flow
For smooth pipe, ε/D = 0
From Moody’s chart…..
f = 0.003

8. 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 )=
∆P= kPa

9. 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 =
We know,
v =(Q/A)= /D2
and ∆P = hrg
D = 0.201cm