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

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

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…

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

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

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 = hrg D = 0.201cm