Concept reference

The Extended Energy Equation

C.1Plain-language definition

The extended energy equation is the ledger for a real hydraulic system. Choose two points, total the energy per unit weight at each, add what a pump supplies and subtract what friction and disturbances dissipate. The equation does not know which component is important; careful boundary selection and an honest loss inventory make it useful.

C.2Governing relation or decision logic

z1 + p1/(ρg) + α1V1²/(2g) + Hp − Ht = z2 + p2/(ρg) + α2V2²/(2g) + hL. Every term is metres of fluid (ft of fluid). The kinetic-energy coefficient α is often approximated as 1 for turbulent pipe flow, but that approximation should be visible when profile distortion matters.

C.3The failure to name

The common failure is double-counting: charging an exit loss and also retaining the same residual velocity head, or adding static lift after it is already embedded in boundary heads. A neat equation with poorly defined points is not auditable.

C.4Field review checklist

• Draw and number the two boundaries before substituting values.
• Write the pressure reference, datum and flow direction.
• List every pump, turbine and dissipative element crossed once.
• Check that all retained terms have dimensions of length and that signs match the chosen direction.

C.5Where it fits in the course

The derivation is in §2.1; §2.5 applies it to pump duty.