19.2 Hydraulics Energy and Head Workbook

Build the energy line before calculating

A hydraulics problem is easier when you draw the energy story first. In pressure flow, total energy includes elevation head, pressure head, velocity head, pump head added, turbine head removed if present, and losses. In open-channel flow, the same physical idea applies, but the pressure distribution, free surface, channel slope, and critical-depth controls change the setup. The PE WRE exam rewards candidates who recognize the control, not candidates who memorize isolated equations.

Head term checklist

Start every energy problem with two stations. Label upstream and downstream conditions, then decide what is known at each station. If both pipe diameters are equal and the flow is steady, velocity head may cancel. If the diameters differ, it may not. If a reservoir surface is one station, velocity at that large surface is often negligible. If a nozzle or outfall is one station, velocity is usually central.

HGL and EGL discipline

The hydraulic grade line is elevation head plus pressure head. The energy grade line adds velocity head. In a constant-diameter pipe, the EGL and HGL are parallel, separated by velocity head. At a pump, both jump upward. Through losses, both drop. In open-channel flow, the water surface often represents the HGL, but transitions, hydraulic jumps, and controls require more careful interpretation.

Pipe workflow

1. Determine whether the pipe is under pressure and flowing full.
2. Write continuity to connect flow, area, and velocity.
3. Select the headloss model appropriate to the information provided.
4. Add minor losses only where the problem gives or implies them.
5. Add pump head if the pump is in the path.
6. Solve for the requested head, pressure, elevation, flow, or power.

Channel workflow

For open channels, first ask whether the problem is normal depth, critical depth, gradually varied flow, hydraulic jump, culvert control, weir flow, or orifice flow. Manning problems often ask for normal flow under uniform assumptions. Critical flow asks where specific energy is minimum. Weir and orifice questions depend on the control geometry and head over the control.

Reasonableness matters. A velocity that is far too high for a gravity sewer, a negative pressure where the system should remain pressurized, or a water-surface profile that climbs through a loss without added energy should trigger review before choosing an answer.

Mini energy sketch drill

For every hydraulics practice problem, make a ten-second sketch before calculating. Mark the upstream station, downstream station, datum, pressure condition, velocity change, pump or control, and major loss reach. If the sketch shows no added energy, the total energy should not rise downstream. If the problem asks for pump head, isolate the pump term after writing losses. This sketch habit is especially useful when answer choices include pressure, head, power, and elevation values that look numerically plausible but represent different physical quantities.