12.4 Head Loss, C-Factor & Distribution Hydraulic Calculations

Components of Head

Head is energy per unit weight of water, expressed in feet. Three components make up total head at any point:

$\text{Total Head} = z + (p \times 2.31) + \frac{v^{2}}{2g}$

Key conversions to have automatic:

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

Static vs Dynamic Pressure

Static and Dynamic Pressure is its own blueprint sub-topic:

• Static pressure is measured with no flow. It equals the elevation difference to the controlling water surface, converted to psi.
• Dynamic (residual) pressure is measured while water is flowing. It is always lower than static, because friction has consumed head.

$\text{Dynamic Pressure} = \text{Static Pressure} - \text{Head Loss (converted to psi)}$

The difference between the two at a given flow is the head loss, which is why a hydrant flow test is fundamentally a head loss measurement.

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Hazen-Williams and the C-Factor

The Hazen-Williams equation is the standard tool for water distribution:

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

where h_f is head loss in feet, L is length in feet, Q is flow in gpm, C is the Hazen-Williams roughness coefficient, and D is inside diameter in inches.

You will rarely be asked to grind through the full equation on an exam. You will be asked about the relationships it encodes:

Worked example. A cast iron main's C-factor has degraded from 130 to 65 through tuberculation. What happens to head loss at the same flow?

Ratio = (130 / 65)^1.85 = 2.0^1.85 ≈ 3.6

Head loss is 3.6 times greater, which means either the far end loses pressure or the pumps burn 3.6 times the friction energy to deliver the same flow. This is the arithmetic that justifies main cleaning and lining programs.

Typical C-Factors

[!TIP] C-factor is a measured property, not a table lookup. A field C-factor test - isolate a length of main, measure flow, measure pressure at two points a known distance apart, and back-calculate C - tells you whether a specific main is worth cleaning. A parallel main installed next to a main that just needed cleaning is an expensive mistake.

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Minor Losses

Fittings, valves, bends, and sudden changes in area also consume head:

$h_m = K \times \frac{v^{2}}{2g}$

In long transmission mains minor losses are negligible. Inside a pump station, a booster station, or a treatment plant they can dominate, which is why a station with an undersized suction header and a partially closed valve can starve a pump that looks correctly sized on paper.

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Velocity and Continuity

$Q = A \times V$

where Q is flow, A is cross-sectional area, and V is velocity. In consistent operator units:

$Q_{\text{gpm}} = 2.448 \times D^{2}_{\text{(in)}} \times V_{\text{(ft/s)}}$

Worked example. An 8-inch main carrying 900 gpm. V = 900 / (2.448 x 64) = 900 / 156.7 = 5.74 ft/s

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The Hydraulic Grade Line

The hydraulic grade line (HGL) is the elevation to which water would rise in an open tube at any point - elevation head plus pressure head. It is the single most useful mental picture in distribution hydraulics:

• The HGL starts at the water surface of the controlling storage.
• It slopes downward in the direction of flow, and the steepness of the slope is the friction loss per unit length.
• Pressure at any point = (HGL elevation − ground elevation) x 0.433.
• A pump adds head, stepping the HGL up. A PRV drops the HGL to a controlled value.
• Where the HGL falls to within 46 feet of ground elevation, pressure has fallen to 20 psi and you are at the regulatory floor.

Worked example. A tank water surface sits at 500 ft. A customer 9,000 ft away at ground elevation 410 ft is served through a main with a friction slope of 3.5 ft per 1,000 ft at the current flow. Friction loss = 9,000 / 1,000 x 3.5 = 31.5 ft HGL at the customer = 500 - 31.5 = 468.5 ft Pressure = (468.5 - 410) x 0.433 = 58.5 x 0.433 = 25.3 psi

That customer is legal but marginal. Increase the flow, or let the tank drop 12 feet, and this service falls below 20 psi.