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Bernoulli’s Equation, the Energy Grade Line, and Real Pipe Losses
p/ρg + V²/2g + z is conserved only without friction. How to draw HGL/EGL, add pump head, and fold in Darcy plus minor losses.
Updated 16 August 2026Solver360 Hydraulics10 min read
Key takeaways
- Bernoulli heads: pressure, velocity, elevation — all in metres of fluid.
- EGL = HGL + V²/2g. HGL is the piezometric line p/ρg + z.
- Real pipes: H1 + H_pump = H2 + h_f + h_m + H_turbine.
- If HGL drops below the pipe, you have a vacuum and a cavitation risk.
Bernoulli’s equation is energy per unit weight along a streamline. In a pipe we write it between two sections and, for real fluids, we add pump work and subtract losses.
The ideal statement
p/ρg + V²/(2g) + z = constant
HGL and EGL
- Hydraulic grade line (HGL): z + p/ρg. The height water would rise in a piezometer.
- Energy grade line (EGL): HGL + V²/2g. The total head.
- In a constant-diameter pipe, EGL and HGL are parallel, V²/2g apart.
- A pump jumps both lines up; a turbine drops them; friction slopes EGL down.
The engineering form
p1/ρg + V1²/2g + z1 + H_pump = p2/ρg + V2²/2g + z2 + h_f + h_m + H_turbine
h_f is Darcy-Weisbach. h_m is ΣK V²/2g. A siphon is this equation with p1 = p2 = Patm and a crown section in between where p may go sub-atmospheric.
Open solver: Friction term h_fOpen solver: Pump head on the EGLOpen solver: Siphon (Bernoulli over a crown)Frequently asked questions
Unsteady flow, compressible flow at high Mach, and non-uniform velocity (use a kinetic-energy correction α). Friction is not “invalid Bernoulli” — it is Bernoulli plus a loss term.
Keywords
bernoulli equation calculatorenergy grade linehydraulic grade linevelocity headpressure headbernoulli with frictionpump head bernoulli
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