Velocity Head Calculator

At a glance:Velocity head (symbol h_v) is the hydraulic quantity that converts the kinetic energy of a flow into an equivalent water-column height. Bernoulli's equation expresses the total energy per unit weight of fluid as the sum of three heads: pressure head (p/γ), elevation head (z) and velocity head (v²/2g), all with unit metres (m) so they add directly into 'total head'. The velocity head formula is h_v=v²/(2g), where v is the velocity (m/s) and g the gravitational acceleration (9.81 m/s²). Its physical meaning: if a stream at speed v converts all its kinetic energy losslessly into height (e.g. shoots straight up to rest), the height it reaches is exactly h_v; conversely, water falling freely from height h_v reaches final speed v — the inverse of Torricelli's law v=√(2gh). Term by term: the numerator v² shows kinetic energy scales with the square of speed, so doubling the speed makes the velocity head four times larger; the denominator 2g normalises kinetic energy into a height unit. Example: v=3 m/s → h_v=3²/(2×9.81)=9/19.62≈0.459 m, meaning this flow's kinetic energy equals the potential of a ~0.459 m water column. Applications: (1) pipe energy analysis — when computing head loss along a line, the velocity head must be included in each section's energy; (2) Pitot-tube speed measurement — the difference between the 'stagnation head' and the 'static head' is exactly the velocity head, from which v=√(2g·h_v); (3) pump and pipe-system design — head and energy balance must contain the kinetic term; (4) open-channel specific energy — the v²/2g in E=y+v²/2g is the velocity head. Notes: (1) v is usually the section average; strictly the kinetic head needs a 'kinetic-energy correction factor' α (laminar α=2, turbulent α≈1.03–1.1, engineering often uses 1) to correct for non-uniform velocity profile; (2) at higher speeds the velocity head dominates the total head, while it is often negligible in low-speed pipe flow; (3) use consistent units (v in m/s) to get head in m.