10.2 Pipe Flow Losses, Pumps, and Net Head
Key Takeaways
- Major losses come from pipe length and friction; minor losses come from entrances, exits, bends, valves, meters, expansions, contractions, and fittings.
- Darcy-Weisbach is a general pipe-loss method, while Hazen-Williams is an empirical water-pipe method that should stay within its assumptions.
- Total dynamic head includes static lift, pressure requirements, velocity-head changes, and all major and minor losses at the selected flow.
- Pump horsepower increases with flow, head, and lower efficiency; the PE WRE shortcut is bhp = Q(gpm)H(ft)/(3960 efficiency).
- Net positive suction head is an absolute-pressure check, so vapor pressure, suction losses, atmospheric pressure, and wet-well level all matter.
Pipe Systems as Resistance Plus Added Head
Closed-conduit items in the current WRE specification include pressure conduits, force mains, Hazen-Williams, Darcy-Weisbach, major and minor losses, pump application, wet wells, lift stations, cavitation, and networks. The common structure is simple: pipes consume head, pumps add head, and the operating point is where the pump can supply exactly what the system requires at that flow.
Loss Types
| Loss type | Typical expression | PE WRE use |
|---|---|---|
| Major loss | h_f = f(L/D)V^2/(2g) | General friction loss with Darcy-Weisbach |
| Minor loss | h_m = K V^2/(2g) | Entrances, exits, bends, valves, fittings, meters |
| Hazen-Williams | Empirical water-pipe loss | Water distribution or force-main screening when allowed |
| Static head | Elevation difference | Reservoir, wet well, tank, or discharge elevation change |
| Pressure head | p/gamma | Required residual pressure or discharge pressure |
Darcy-Weisbach is broadly applicable because it is dimensionally consistent and connects to friction factor, roughness, Reynolds number, and relative roughness. Hazen-Williams is common for ordinary water-pipe calculations, but it is empirical. Do not use it casually for air, viscous fluids, or conditions outside normal water-system practice.
Minor losses are not always minor. In a short pump station header, valve vault, meter run, or culvert entrance, the sum of K values can be a large fraction of the total head. The exam may give K values directly or ask which fitting change increases loss most. Since minor loss varies with V^2, reducing diameter can raise losses quickly.
Total Dynamic Head Workflow
- Set the design flow and convert all units.
- Compute velocity in each pipe reach.
- Add static elevation difference between supply and discharge energy levels.
- Add any required pressure head at the delivery point.
- Add major losses and minor losses at the design flow.
- Include velocity-head differences if pipe sizes or discharge conditions differ.
- Compare total dynamic head with the pump curve at the same flow.
For pumps, power is the rate of energy addition. In US customary water problems, water horsepower is Q(gpm)H(ft)/3960. Brake horsepower divides by pump efficiency as a decimal. A 70 percent efficient pump needs more brake horsepower than water horsepower because some input energy becomes heat, noise, and mechanical loss.
Net Head and Cavitation
Net positive suction head available, usually NPSHa, is a suction-side absolute-head margin above vapor pressure. For an open wet well, NPSHa generally starts with atmospheric pressure head, adds the water surface elevation relative to the pump datum if the surface is above the pump, subtracts suction-pipe losses, and subtracts vapor pressure head. A hot liquid has higher vapor pressure and less margin. A lower wet-well level also reduces margin. Cavitation can damage impellers and reduce capacity, so a design should keep NPSHa greater than the pump manufacturer's NPSH required with a reasonable margin.
Lift stations combine pump and wastewater constraints. A larger force main reduces headloss and horsepower, but velocities that are too low can allow solids deposition. A smaller force main improves scouring velocity but raises headloss and energy cost. The WRE exam may test that tradeoff conceptually rather than asking for a full life-cycle cost.
Series, Parallel, and Loops
In series pipes, the same flow passes through every segment and headlosses add. In parallel branches, each branch has the same node-to-node headloss and flow splits according to resistance. A rougher, longer, smaller branch carries less flow under the same headloss. Loop networks require continuity at nodes and compatible headloss around loops. Even without performing a full network iteration, you should be able to reject a proposed flow split that sends most of the water through the highest-resistance branch.
A 1.0-ft diameter pipe carries 3.14 cfs through 800 ft of pipe. If f = 0.020 and the combined minor-loss coefficient is K = 3.0, what is the approximate total headloss?
A pump delivers 900 gpm against 72 ft of total dynamic head at 70 percent efficiency. Approximately what brake horsepower is required?