My book describes three different cases of turbulent flow problems. The third ca

Question

My book describes three different cases of turbulent flow problems. The third case requires solving for the diameter of the conduit, given the flow rate, length of pipe and head loss. All of the sample problems use an iterative approach in which you estimate the friction factor and use that estimated friction factor throughout the problem over and over until the velocities match. In most of the problems, they estimate the friction factor to be f=.015. How do they estimate this? Is it the same estimate for all the problems?

Explanation / Answer

first we need to find the reynolds number then we can estimate the value of friction factor by using the differnet formulas..when it is laminar , when it is turbulent..in turbulent there are two cases turbulent flow in smooth and rough pipe friction factor value changes..
Be able to determine a value of the Moody friction factor from the
Moody diagram, for given Re and /D.
For laminar flow (Reynolds number, R 2100), the friction factor is linearly

dependent on R, and calculated from the well-known Hagen-Poiseuille equation:

=64/R

In a smooth pipe flow, the viscous sub layer completely submerges the effect of k
on the flow. In this case, the friction factor is a function of R and is independent of the
effect of k on the flow. Nikuradse (1933) had verified the Prandtl’s mixing length theory
and proposed the following universal resistance equation for fully developed turbulent
flow in smooth pipe;

1/= 2 log (R ) 0.8

In case of rough pipe flow, the viscous sub layer thickness is very small when
compared to roughness height and thus the flow is dominated by the roughness of the
pipe wall and is the function only of k/D and is independent of R. The following form
of the equation is first derived by Von Karman (Schlichting, 1979) and later supported by
Nikuradse’s experiments;

1/=2log(D/k)+1.74

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