Equation
Number
Author [Reference]
Explicit Models
Applicable Range of Re and ε/D
Classification
2
Romeo, Royo and Monzon [9]
3 × 103 ≤ Re ≤ 1.5 × 108
0 ≤ ε/D ≤ 5 × 10−2
Extremely
accurate
3
Serghides [15]
, 
, 
, 
Not specified
Extremely
accurate
4
Chen [11]
4 × 103 ≤ Re ≤ 4 × 108
10−7 ≤ ε/D ≤ 5 × 10−2
Very accurate
5
Buzzelli [16]
; where
, 
3 × 103 ≤ Re ≤ 3 × 108
0 ≤ ε/D ≤ 5 × 10−2
Extremely
accurate
6
Zigrang and Sylvester [14]
4 × 103 ≤ Re ≤ 108
4 × 10−5 ≤ ε/D ≤ 5 × 10−2
Extremely
accurate
7
Barr [19]
Not specified
Very accurate
8
Fang, Xu, Zhou [13]
3 × 103 ≤ Re ≤ 1.5 × 108
0 ≤ ε/D ≤ 5 × 10−2
Very accurate
9
Shacham [20]
4 × 103 ≤ Re ≤ 4 × 108
Moderately
accurate
10
Sonnad and Goudar [21]
; where 
4 × 103 ≤ Re ≤ 108
10−6 ≤ ε/D ≤ 5 × 10−2
Moderately
accurate
11
Manadilli [23]
5.235 × 103 ≤ Re ≤ 108
0 ≤ ε/D ≤ 5 × 10−2
Less accurate
12
Ghanbari, Farshad and Rieke [17]
2.1 × 103 ≤ Re ≤ 108
0 ≤ ε/D ≤ 5 × 10−2
Less accurate
13
Churchill [24]
; where
, 
Re > 0
0 ≤ ε/D ≤ 5 × 10−2
Less accurate