Supplementary Material, Appendix 0 – A0.32

APPENDIX 0 – Pre-requisite: Steady State Hydraulics

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Surge Analysis and the Wave Plan Method

Supplementary Material: Example Problems and Solutions

Appendix 0 – Problem 32

A0.32 Consider a short ductile iron (DI) pipe section of 6m length and 300 mm internal diameter. Compute the total friction headloss and unit friction headloss (friction headloss per 1000m length) in this pipe section when the flow velocity is 2 m/s using Darcy-Weisbach equation with the 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 friction factor, L is length of pipe section, V is mean flow velocity, g is gravitational acceleration, and D is pipe internal diameter; all parameters in standard English or SI units.

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

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

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

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

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

For E = 0.00012m, D = 0.3m, V = 2 m/s, 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) = 0.0689m

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

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


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