Explain the term coefficient of friction. On what factors does this coefficient depend?

Co - efficient of friction :

Loss of head due to friction in pipe is

$h_f = \frac{4fLv^2}{d \times 2g}$

here, the value of co-efficient of friction, (f) should be known accurately for predicting the loss of head due to friction in pipes.

On the basis of dimensional analysis, it can be shown that the pressure loss in straight pipe of diameter D, Length L, roughness K, average velocity of flow ū, viscosity and density of fluid $\mu$ and $\rho$ is,

$\triangle p = \frac{\rho ū ^2}{2} \times \phi [Re, \frac{K}{D}, \frac{L}{D}] $

i.e,

$\frac{\triangle p}{(\rho ū^2/2)} = \phi [Re , \frac{K}{D}, \frac{L}{D}] $

Experimentally it was found that pressure drop is a function of ${L}{D}$ to the first power and hence,

$\triangle p = \frac{\rho ū ^2}{2} = \frac{L}{D} \phi [Re , \frac{K}{D}]$

The term of the right hand side is called as co-efficient of friction f.

Thus $f = \phi [Re , \frac{K}{D}]$

This equation shows that friction co-efficient is a function of Reynold number and K/D ratio, where,

K - average height of pipe wall roughness protrusions.

Factors on which co-efficient of friction (f) depends on :

1) Reynold number

2) $\frac{K}{D}$

For laminar flow, $f = \frac{16}{Re}$ only dependents on Re.

For Turbulent flow :

' F ' for smooth pipes = $\frac{0.0791}{(Re) ^{1/4}}$ (Blasius).