FLOWS IN PIPING SYSTEMS : Table of the resistance coefficients C
The Hazen–Williams and Chezy–Manning relations are valid over a limited
range of Re while Darcy-Weissbach formulation provides a more versatile and
accurate estimate of pipe losses.
,FLOWS IN PIPING SYSTEMS : Table of the resistance coefficients C
In the following Table the values of the Manning coefficient n
for different materials are reported, the units of
measurements are T/L(1/3); s/m(1/3)
, FLOWS IN PIPING SYSTEMS : Example 1
A pipeline is conveying 0.05 m3/s of water, at 30C. The length of the line is 300
m, and the diameter is 0.25 m. Estimate the head loss due to friction using the
three formulas (a) Darcy–Weisbach (e = 0.5 mm), (b) Hazen–Williams (C = 110),
and (c) Chezy–Manning (n = 0.012). The kinematic viscosity of water at 30C is
n = 0.804 x 106 m2/s.
Solution scheme:
1-Calculate the following quantities: relative roughness e/d; average velocity V;
Reynolds number Re:
𝑒 𝑄 1.02𝑚 𝑉𝐷
= 0.002; 𝑉 = = ; 𝑅𝑒 = = 3.17 ∙ 105
𝐷 𝐴 𝑠 𝜐
2-substitute in the formula and find R for DW formulation:
300 −2
𝑅 = 1.07 5
𝑙𝑛 0.27 ∙ 0.002 + 5.74 3.17 ∙ 105 −0.9 = 610
9.81 ∙ 0.25
The Hazen–Williams and Chezy–Manning relations are valid over a limited
range of Re while Darcy-Weissbach formulation provides a more versatile and
accurate estimate of pipe losses.
,FLOWS IN PIPING SYSTEMS : Table of the resistance coefficients C
In the following Table the values of the Manning coefficient n
for different materials are reported, the units of
measurements are T/L(1/3); s/m(1/3)
, FLOWS IN PIPING SYSTEMS : Example 1
A pipeline is conveying 0.05 m3/s of water, at 30C. The length of the line is 300
m, and the diameter is 0.25 m. Estimate the head loss due to friction using the
three formulas (a) Darcy–Weisbach (e = 0.5 mm), (b) Hazen–Williams (C = 110),
and (c) Chezy–Manning (n = 0.012). The kinematic viscosity of water at 30C is
n = 0.804 x 106 m2/s.
Solution scheme:
1-Calculate the following quantities: relative roughness e/d; average velocity V;
Reynolds number Re:
𝑒 𝑄 1.02𝑚 𝑉𝐷
= 0.002; 𝑉 = = ; 𝑅𝑒 = = 3.17 ∙ 105
𝐷 𝐴 𝑠 𝜐
2-substitute in the formula and find R for DW formulation:
300 −2
𝑅 = 1.07 5
𝑙𝑛 0.27 ∙ 0.002 + 5.74 3.17 ∙ 105 −0.9 = 610
9.81 ∙ 0.25
