Hydraulic_head - Wikiparency

# Hydraulic head **Hydraulic head** is the mechanical [[Energy|energy]] per unit weight of a liquid, expressed as a height. In a pipe or an aquifer it is measured by the level to which water rises in an open tube, a piezometer: h = z + p/ρg, the elevation of the point plus its pressure head. Adding the velocity head v²/2g gives the total head of [[Bernoulli's_principle|Bernoulli's principle]], and the fall of head along a flow is the energy friction has spent.[^up1-14][^barmeir-11] Head is the quantity every [[Hydropower|hydropower]] site sells and every pump buys, and in the ground it is what drives [[Groundwater|groundwater]]. <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Hydraulic_head.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" allow="accelerometer; gyroscope" title="Hydraulic head — p5.js microsim"></iframe> </div> *Microsim (THY-038): open a valve on a pipe fed from a tank; piezometer tubes along the pipe trace the hydraulic grade line, which falls with friction h_f = f(L/D)v²/2g. ILLUSTRATIVE: constant friction factor and a fixed tank level.* Videos: [16:9](https://wikitube-3d-microsims.netlify.app/media/Hydraulic_head_16x9.mp4) · [9:16](https://wikitube-3d-microsims.netlify.app/media/Hydraulic_head_9x16.mp4) ## Definition For a liquid of [[Density|density]] ρ, the hydraulic (piezometric) head at a point is h = z + p/(ρg), with z the elevation above a datum, p the gauge pressure and g the acceleration of [[Gravity|gravity]]. The total head adds the kinetic term: H = z + p/(ρg) + v²/(2g). In steady flow without losses H is constant along a streamline — Bernoulli's equation divided by ρg.[^up1-14] ## Components Elevation head is the potential energy per unit weight; pressure head is the height of liquid column the pressure could support; velocity head is the height through which the liquid would have to fall to reach its speed. In a still tank all the head is elevation plus pressure, and every piezometer stands at the same level as the tank surface. ### Fresh water head Where water of different densities is involved, as with salt and fresh groundwater, heads are often converted to an equivalent fresh-water head so that they can be compared. ## Hydraulic gradient The hydraulic gradient is the change of head per unit distance along a flow path. In a pipe it sets the friction the flow must overcome; in the ground, Darcy's law makes the flow proportional to it.[^zeidouni] ## In groundwater In an aquifer the velocity head is negligible, so the head is the level water stands at in a well. Groundwater flows from high head to low head, and maps of head, drawn from well levels, show which way it moves.[^theis-water] ### Atmospheric pressure Heads are normally measured with gauge pressure, relative to the atmosphere, so that a free water surface has zero pressure head. ## Head loss Friction turns part of the head into heat as water flows. In a pipe, the Darcy–Weisbach equation gives the loss as h_f = f(L/D)v²/(2g), where f is the friction factor from the Moody diagram or the Colebrook–White equation.[^barmeir-11] Bends, valves and entrances add minor losses proportional to v²/2g. For a hydropower plant, the head delivered to the turbine is the gross head minus these losses. ## See also - [[Bernoulli's_principle]] - [[Hydrostatics]] - [[Penstock]] - [[Groundwater]] - [[Aquifer]] ## References [^up1-14]: Ling, Samuel J.; Sanny, Jeff; Moebs, William (2016). *University Physics, Volume 1*, ch. 14 "Fluid Mechanics" (§14.6 Bernoulli's equation). OpenStax. https://openstax.org/details/books/university-physics-volume-1 [^barmeir-11]: Bar-Meir, Genick (2025). *Basics of Fluid Mechanics*, version 0.7.5, ch. 11 (pipe flow; Darcy–Weisbach friction factor, Moody diagram). https://open.umn.edu/opentextbooks/textbooks/basics-of-fluid-mechanics [^zeidouni]: Zeidouni, Mehdi (2025). *Petroleum Reservoir Dynamics*, ch. 2 (Darcy equation), §3.3 (radial flow), ch. 8 (transient radial flow and drawdown). LSU Scholarly Repository. https://open.umn.edu/opentextbooks/textbooks/petroleum-reservoir-dynamics [^theis-water]: Theis, Tom; Tomkin, Jonathan, eds. (2015). *Sustainability: A Comprehensive Foundation*, ch. 7, module "Water Cycle and Fresh Water Supply." https://open.umn.edu/opentextbooks/textbooks/sustainability-a-comprehensive-foundation ### Portal Books - Ling, Sanny & Moebs (2016). *University Physics, Volume 1* — [OpenStax](https://openstax.org/details/books/university-physics-volume-1); on the [[PORTAL_Physics]] shelf. - Bar-Meir, Genick (2025). *Basics of Fluid Mechanics*, v0.7.5 — [OTL record](https://open.umn.edu/opentextbooks/textbooks/basics-of-fluid-mechanics); on the [[PORTAL_WT!Thury_Hydrodynamics_Compendium|Compendium]] Fluid core shelf.  *Linked from the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]], section 15, Hydropower.*   **Microsim — three.js (Wikitube framework):** *Hydraulic head* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Hydraulic_head.html" data-title="Hydraulic head"></div> *Built from `MICROSIM_GUIDE/specs/variants/Hydraulic_head.json`; part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]] set.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Hydraulic_head) : [Wikitube](https://en.wikitube.io/wiki/Hydraulic_head) · pinned revision [1368161580](https://en.wikipedia.org/w/index.php?oldid=1368161580) · 2026-09-10 ## Previous hub tags Hubs: `Life_Physics`, `Systems`. Portals: [[PORTAL_Thury_Hydrodynamics_Apex_Spine]], [[PORTAL_Energy]], [[PORTAL_Physics]]. --- *Thury station wave · 2026-09-10 · drafted · microsim THY-038 (p5.js) · parent [[Hydropower]].*