Friction loss in water pipes can be obtained by using the empirical Hazen-Williams equation
Hazen-Williams Equation
f = 0.2083 (100/C)1.852 Q1.852/ d4.8655
Where
• f = friction head loss in feet of water per 100 feet of pipe
• C = Hazen-Williams roughness constant
• Q = volume flow (gal/min)
• d = inside diameter (inches)
Note that the Hazen-Williams formula is empirical and lack s physical basis. Be aware that the roughness constants are based on "normal" condition with approximately 3 ft/sec.
Darcy-Weisbach equation and Head Loss
The Darcy-Weisbach equation is valid for fully developed, steady, incompressible flow. The friction factor or coefficient -depends on the flow - if it is laminar, transient or turbulent (the Reynolds Number) - and the roughness of the tube or duct. The friction coefficient can be calculated by the Colebrook e Equation or by using the Moody Diagram.
Alternatively the Darcy-Weisbach equation can be expressed as head loss:
H loss = λ (L / dn) [v2/ (2 x g)]
Where
• H loss H = head loss (ft)
• λ = friction coefficient
• L = length of duct or pipe (ft)
• g = acceleration of gravity (32.2 ft/s2 )
• dn = The hydraulic diameter - dh - is used for calculating the dimensionless Reynolds
Number (Re) to determine if the flow is turbulent or laminar.
The Reynolds Number (Re) is important in analyzing any type of flow when there is substantial velocity gradient - shear. The Reynolds Number indicates the relative significance of the viscous effect compared to the inertia effect. The Reynolds number is proportional to inertial force divided by viscous force. The flow is
‹ laminar if Re <> 4000
Reynolds Number can be expressed as:
Re = D x v x ρ / µ
Where
• D = characteristic length (For a pipe or duct the characteristic length is the pipe or duct diameter, in m)
• v = velocity (m/s)
• ρ = density (kg/m3 )
• µ = dynamic (absolute) viscosity (Ns/m2 )
Hydraulic Diameter: The hydraulic diameter is not the same as the geometrical diameter in non- circular ducts or pipes and can be calculated from the generic equation:
dh = 4 A / P
Where:
• dh = hydraulic diameter (in)
• A = area section of the pipe (in2 )
• P = wetted perimeter of the pipe (in)
Friction Coefficient (λ) for fully developed laminar flow the roughness of the duct or pipe can be neglected. The friction coefficient depends only the Reynolds Number -Re - and can be expressed as:
λ= 64 / Re
Where
• Re = the dimensionless Reynolds number
