10.2 Pipe Flow Losses, Pumps, and Net Head

Pipe Systems as Resistance Plus Added Head

Closed-conduit items on the WRE specification include pressure conduits, force mains, the Hazen-Williams and Darcy-Weisbach methods, major and minor losses, pump application, wet wells, lift stations, cavitation, and pipe networks. The unifying structure is simple: pipes consume head, pumps add head, and the operating point is the flow at which the pump curve and the system curve intersect. The system curve is static head plus a friction term that grows roughly with Q^2; the pump curve is head that falls as flow rises. Their intersection is where the system actually runs.

Loss Types

Darcy-Weisbach is broadly applicable because it is dimensionally consistent and ties directly to the friction factor f, which depends on Reynolds number and relative roughness (read from the Moody diagram in the handbook). Hazen-Williams uses a roughness coefficient C (e.g., C is about 130-150 for new PVC or cement-lined ductile iron, ~100 for older cast iron). It is calibrated for turbulent water flow near 60 degF; do not apply it to air, viscous fluids, or conditions outside ordinary water practice.

Minor losses are not always minor. In a short pump-station header, valve vault, meter run, or culvert entrance, the summed K values can be a large fraction of TDH. The exam may give K values directly or ask which fitting change increases loss most. Since h_m varies with V^2, shrinking a diameter raises both V and the loss steeply (V^2 scales with 1/D^4).

Total Dynamic Head Workflow

1. Fix the design flow Q and convert all units to one system.
2. Compute velocity V = Q/A in each pipe reach.
3. Add the static elevation difference between supply and discharge energy levels.
4. Add any required residual pressure head at the delivery point.
5. Add major and minor losses at the design flow.
6. Include velocity-head differences if pipe sizes or discharge conditions differ.
7. Match TDH against the pump curve at the same flow.

For pumps, power is the rate of energy addition. In US customary water problems, water horsepower (whp) = Q(gpm) x H(ft) / 3960 and brake horsepower (bhp) = whp / efficiency. The constant 3960 already bundles the specific weight of water and unit conversions. A 70 percent efficient pump needs more bhp than whp because input energy also becomes heat, noise, and mechanical loss. Motor input power adds another division by motor efficiency.

Net Head and Cavitation

Net positive suction head available (NPSHa) is a suction-side absolute-head margin above the liquid's vapor pressure. For an open wet well it is built as: atmospheric pressure head (h_atm) plus or minus the surface elevation relative to the pump (h_s, positive if the surface is above the pump) minus suction-pipe losses (h_L) minus vapor pressure head (h_vp): NPSHa = h_atm +/- h_s - h_L - h_vp. A hotter liquid has a higher vapor pressure and less margin; a lower wet-well level also cuts margin.

Cavitation pits impellers and reduces capacity, so design keeps NPSHa above the manufacturer's NPSH required (NPSHr) by a margin, commonly a few feet.

Lift stations couple pump and wastewater constraints. A larger force main lowers headloss and energy, but velocity that is too low (below roughly 2 ft/s) lets solids settle. A smaller force main keeps a scouring velocity but raises headloss and energy cost. The exam often tests this tradeoff conceptually rather than as a full life-cycle cost.

Series, Parallel, and Loops

In series, the same Q passes through every segment and headlosses add. In parallel branches, every branch sees the same node-to-node headloss and flow splits by resistance; a rougher, longer, smaller branch carries less flow. Loop networks (Hardy Cross) enforce continuity at nodes and zero net headloss around each loop. Even without a full iteration, reject any proposed split that routes most flow through the highest-resistance branch.

System Curve and Operating Point

The single most-tested pump concept is the operating point. The system curve plots required head versus flow: H_sys = H_static + C Q^2, where H_static is the elevation lift plus required pressure head (fixed, independent of Q) and the C Q^2 term captures friction and minor losses (zero at zero flow, rising steeply with flow). The pump curve plots head the pump can deliver versus flow and slopes downward. Their intersection is the operating point, the only flow and head at which the pump and system are simultaneously satisfied.

Useful consequences the exam exploits: closing a discharge valve adds resistance, steepening the system curve, so the operating point slides up and left to a lower flow at higher head. Two identical pumps in parallel roughly double the flow at a given head (heads equal, flows add), which helps on a flat system curve but barely helps on a steep, friction-dominated one. Two identical pumps in series roughly double the head at a given flow (flows equal, heads add), which helps on steep system curves.

The affinity laws relate a single pump at variable speed: flow scales with speed (Q ~ N), head with speed squared (H ~ N^2), and power with speed cubed (P ~ N^3), so a 20 percent speed reduction cuts power by nearly half. Expect at least one item asking how an operating point shifts when a valve, a parallel pump, or a speed change is introduced.