Supplementary Material 0.2

Chapter 0 – Steady-State Hydraulics

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Supplementary Material: Example Problems and Solutions

Chapter 0 – Problem 0.2

0.2 Consider a short ductile iron (DI) pipe section of 6 m length and 300 mm internal diameter. Compute the total friction headloss and unit friction headloss (friction headloss per 1000 m length) in this pipe section at a velocity of 2 m/s using the Darcy-Weisbach equation and a manufacturer-suggested roughness element size of 0.12 mm.

Solution:

The Darcy-Weisbach equation in its simplest form for friction headloss in a pipe section is:

ΔH = (f L V2) / (2 g D), where f is the friction factor, L is the length of the pipe section, V is the mean flow velocity, g is the gravitational acceleration, and D is the pipe internal diameter; all parameters are in standard English or SI units.

The friction factor f depends on the flow regime (i.e., laminar, turbulent, or transition, which in turn are governed by the Reynolds number), pipe roughness, and internal diameter.

The Colebrook-White equation provides the most accurate estimate for the friction factor:

where  is the size of the pipe internal roughness in ft or m ( /D is referred to as the relative roughness) and Rn is the Reynolds number.

The Reynolds number Rn is calculated using the equation Rn = VD/ν, where ν (i.e., the Greek letter nu) is the kinematic viscosity of the fluid in standard English units (ft2/s) or standard SI units (m2/s).

The Colebrook-White equation is an implicit equation requiring an iterative solution. The explicit equation for friction factor calculations most widely used by water utilities is the Swamee-Jain equation:

For  = 0.00012 m, D = 0.3 m, V = 2 m/s, and ν = 0.000001 m2/s, the Reynolds number Rn = 599993 and the friction factor f = 0.0169.

ΔH = (f L V2) / (2 g D) = (0.0169 * 6 * 22) / (2 * 9.81 * 0.3) = 0.0689 m

This friction headloss of 0.0689 m is in the 6 m section of the DI pipe.

ΔH per 1000 m of pipeline = (0.0689/6) * 1000 = 11.53 (m/km)

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