15.5 Distribution Hydraulics, Head Loss & C-Factor

15.5 Distribution Hydraulics, Head Loss & C-Factor

Distribution hydraulics is where the calculation items concentrate on the Water Distribution exam. The Need-to-Know Criteria require operators to "understand flow characteristics (e.g., diameter, C-factor, head loss, linings, fittings, flow rate)," "determine water volume," and "determine water flow rate."

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The Two Conversions You Cannot Get Wrong

$1\text{ ft of head} = 0.433\text{ psi} \qquad 1\text{ psi} = 2.31\text{ ft of head}$

Worked example. A tank's water surface sits 145 ft above a service connection.

$145 \times 0.433 = 62.8\text{ psi}$

Working backward, a pressure gauge reading 55 psi corresponds to 55 × 2.31 = 127 ft of head.

[!IMPORTANT] Mixing these up is the most common arithmetic error in the distribution section. Remember the direction physically: a foot of water is a small amount of pressure (less than half a psi), so converting feet to psi must make the number smaller. Converting psi to feet makes it larger.

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Pressure Terms

Pressure Requirements

Falling below 20 psi risks backsiphonage of contaminants into the main and typically triggers a boil-water advisory and regulatory notification.

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Flow and Velocity

$Q = A \times V$

where Q is flow, A is cross-sectional area, and V is velocity.

$A = 0.785 \times D^2 \quad \text{(D in feet)}$

Worked example. A 12-inch main carries 1,800 gpm. What is the velocity?

Convert flow to cubic feet per second: 1,800 gpm ÷ 448.8 = 4.01 cfs. Area: 0.785 × (1.0 ft)² = 0.785 ft².

$V = \frac{4.01}{0.785} = 5.1\text{ ft/s}$

Design guidance: normal distribution velocities run about 2 to 5 ft/s. Below roughly 2 ft/s, sediment settles and water age increases. Above about 5 to 7 ft/s, head loss becomes excessive, scouring may release deposits and cause discolored water, and the risk of surge on valve closure rises.

Useful conversions:

$1\text{ cfs} = 448.8\text{ gpm} \qquad 1\text{ MGD} = 694.4\text{ gpm} = 1.547\text{ cfs}$

Pipe Volume

$\text{Volume (gal)} = 0.785 \times D^2 \times L \times 7.48$

Worked example. An 8-inch main, 2,400 ft long. D = 8/12 = 0.667 ft.

$0.785 \times 0.667^2 \times 2,400 \times 7.48 = 0.785 \times 0.445 \times 2,400 \times 7.48 = 6,270\text{ gal}$

This calculation drives chlorination volumes for main disinfection and flushing durations.

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The Hazen-Williams C-Factor

The C-factor describes the interior smoothness of a pipe. Higher C means smoother pipe and less friction loss.

Tuberculation — the buildup of corrosion nodules on unlined iron pipe — is the primary cause of C-factor decline. Its effects compound: the deposits roughen the wall and reduce the effective diameter, so a badly tuberculated 8-inch main may behave hydraulically like a 5-inch pipe.

The Hazen-Williams relationship (for head loss in feet per 1,000 ft):

$h_f = \frac{10.44 \times L \times Q^{1.85}}{C^{1.85} \times D^{4.87}}$

with L in feet, Q in gpm, and D in inches. You will rarely compute this by hand on the exam, but the proportionalities matter:

• Head loss varies with flow raised to about the 1.85 power — roughly the square. Double the flow and friction loss nearly quadruples.
• Head loss varies inversely with diameter to about the 4.87 power — so diameter is enormously influential. Increasing a main from 8 to 12 inches cuts head loss by roughly a factor of seven at the same flow.
• Head loss varies inversely with C to the 1.85 power — halving C roughly quadruples head loss.

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Field C-Factor Testing

The practical field method:

1. Isolate a section of main of known length, diameter, and material.
2. Establish a known, steady flow through it, usually by discharging through a hydrant with a calibrated pitot or flow meter.
3. Measure pressure at two points bracketing the section, correcting for any elevation difference.
4. Convert the pressure difference to feet of head loss.
5. Solve Hazen-Williams for C.

Worked example (interpretation). A 3,000 ft section of 8-inch main flowing 900 gpm shows 27 ft of head loss after elevation correction, which computes to a C of roughly 75. For a main installed as cement-lined ductile iron at C 140, that result indicates substantial interior deterioration and makes the section a candidate for cleaning and lining, or replacement.

C-factor testing is how a utility converts a hunch about "low pressure in that neighborhood" into an engineering justification for capital work.

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Minor Losses

Fittings, valves, and bends add losses beyond straight-pipe friction. These are often expressed as an equivalent length of straight pipe:

[!NOTE] Note how dramatically a partially closed valve adds loss. A single gate valve left half open can impose more head loss than a hundred feet of main, and a partially closed valve is a very common cause of unexplained low pressure in a neighborhood. Valve exercising programs exist partly to find these, and a systematic check of valve positions should precede any conclusion that a main needs replacement.