1.3 Fluid Dynamics
25
Nikuradse formula (Eq. 1.26) (turbulent flow and rough duct) gives:
1
√
f
= −2.0 log
ε
D h
3.71
A = 6.18451
f = 0.02615
Colebrook–White equation (Eq. 1.27) (turbulent flow and intermediate roughness)
gives:
1
√
f
= −2.0 log
ε
D h
3.71
+
2.51
Re
√
f
A = 6.08016
f = 0.02707
USBM approximate expression (Eq. 1.28) (turbulent flow and intermediate
roughness) provides:
1
√
f
= −2.0 log
ε
D h
3.71
+
2.825
Re
√
f
A = 6.06813; f (x) = 8.3489 × 10
−14
f = 0.02716
Haaland’s approximate formula (Eq. 1.29) (turbulent flow and intermediate
roughness):
1
√
f
= −1.8 log
6.9
Re
+
ε
D
3.71
1.11
A = 6.08534
f = 0.02700
The indicated conditions correspond to turbulent flow and medium roughness pipeline, for this reason, von Karman–Prandtl’s expression is not indicated. Moreover, Nikuradse’s expression, despite being indicated for rough
pipelines, approaches Colebrook–White’s expression well enough. Finally,
Haaland and USBM expressions for friction factor, which approximate
the Colebrook–White’s expression offer also significantly accurate results.