Hydraulics–Closed Conduit

Flow in pipes running full: the energy and continuity equations, grade lines and momentum, friction and minor losses, pumps and wet wells, and networks of pipes in series, parallel and loops. It carries 7–11 of the 80 questions on the Water Resources & Environmental exam — one of the heavier areas.

What the problems look like

Mostly calculation, often read off a profile or a pump curve. Recurring shapes — the energy equation between two water surfaces, or to a high point, a siphon crest or a free jet; head loss by Hazen-Williams or Darcy-Weisbach plus fittings; a pump operating point where the pump curve meets the system curve, then power and NPSH available; parallel and series mains and a Hardy Cross loop; and thrust at a bend. Expect profiles to read and HGL/EGL concept checks.

By exam day you should be able to —

• write the energy equation with the right end points, and sketch the HGL and EGL through enlargements, fittings and high points;
• compute major and minor losses (Hazen-Williams and Darcy-Weisbach, laminar and turbulent);
• build a system curve (static lift + losses ∝ Q²), find the operating point, and combine pumps in parallel or series;
• compute water, brake and input power, and NPSHA against cavitation;
• size a wet well from pump cycle time and inflow, and check pump submergence;
• split flow in parallel mains, sum losses in series, and balance a loop;
• resolve the pressure and momentum forces on a bend.

Where people lose points

• Grade-line end points: the pressure at a high point depends on the friction lost before it, not a static head or a length-proportioned guess; a free jet keeps its velocity head, a submerged outlet loses it.
• Minor losses: the entrance and exit count; read the K for the fitting actually named.
• Scaling losses with the wrong power — friction and minor losses go with Q² (Hazen-Williams, Q^1.85), not Q, and a loss quoted at one flow is not a fixed head at another.
• Parallel vs. series: parallel mains share one head loss and add flows; series mains share one flow and add losses. Pair each diameter with its own length, and never average diameters — loss goes as D^−4.87 (Hazen-Williams) or D^−5 (Darcy-Weisbach).
• Pumps: parallel pumps add flow at the same head; the new operating point climbs the system curve, so flow does not double. The affinity laws don't hold along a system curve that has static lift.
• Efficiencies compound — divide by pump × motor efficiency, not their average; keep kW and hp apart.
• Loop sign convention: sign each pipe by its sense around the loop — clockwise positive — not by whether its arrow points right or down; a pipe shared by two loops takes opposite signs in each.

Have these at your fingertips

Hazen-Williams and Darcy-Weisbach in both unit systems, the Moody diagram, minor-loss coefficients, water properties by temperature, and the NPSH relation — plus where they live in the Handbook. The Hardy Cross loop correction is not printed — only network continuity and equal head loss in parallel pipes are — so carry it yourself.

Going deeper

• Drinking Water Distribution and Treatment
• Wastewater Collection and Treatment

Part of the Water Resources & Environmental exam. Practice this area with exam-real problems — the tutor walks any one you miss. → Start practicing free — free with an account.