The equation13is valid for For the rough tube, friction factor is higher than calculated by equation 13. For rough tubes, f depends on surface roughness and Reynold’s number. For a given roughness, f can be determined from charts given in references at the end of this lecture.

For non-circular conduits an equivalent diameter  replaces  in the Reynold’s number

(14)

                                    
For a rectangular duct of cross section

(15)

Enlargement and Contraction
When the fluid enters from the reservoir to the nozzle, there is a sudden contraction. Similarly there is sudden expansion when the fluid exits the nozzle to the environment. Frictional losses in both sudden contraction and sudden expansion can be evaluated from

(16)

where is the fluid velocity in the smaller cross section  is friction factor due to sudden contraction and  is friction factor due to sudden expansion. The values of  and  depend on area ratio and Reynold’s number.

Flow through valves and fittings

The frictional losses associated with the fluid flowing via valves and fittings are evaluated by assigning an equivalent length to the fixture such that the L/D in eq. 10 is given by

(17)