Which statement correctly describes the relationship between the Hydraulic Grade Line (HGL) and the Energy Grade Line (EGL)?

• A. HGL is the piezometric head p/(rho g) + z, while EGL adds velocity head to give p/(rho g) + z + v^2/(2g).
• B. HGL is the piezometric head, and EGL excludes velocity head.
• C. HGL includes velocity head, and EGL is equal to stagnation head.
• D. HGL and EGL are identical.

Answer: (A)

The main idea is that the hydraulic grade line (HGL) represents pressure head plus elevation, while the energy grade line (EGL) adds the velocity head to this, giving the total head. In formulas, HGL = p/(ρg) + z, and EGL = p/(ρg) + z + v^2/(2g). So the statement that HGL is the piezometric head and EGL includes velocity head is the correct description. It means EGL sits higher than HGL by the amount of the velocity head v^2/(2g). The other options misstate one or both parts: HGL does not include velocity head, EGL does include it, and HGL and EGL are not identical.