Compressible_flow - Wikiparency

# Compressible flow **Compressible flow** is the branch of [[Fluid_dynamics|fluid dynamics]] that deals with flows in which the fluid's [[Density|density]] changes significantly. Every real fluid can be squeezed, but for water in a pipe or air around a slow car the change is so small that engineers treat the fluid as incompressible. When a gas moves at a large fraction of the speed of [[Sound|sound]], pressure changes become large enough to change its density, and the flow behaves in new ways: it can choke in a narrow passage, speed up in a widening one, and form shock waves across which pressure, temperature and density jump almost instantly.[^nasa-role][^nasa-normal] The usual rule of thumb is that a flow can often be treated as incompressible when its Mach number is below about 0.3.[^britannica] Compressible flow is not only a subject for aircraft. [[Natural_gas|Natural gas]] moving through a pipeline network, exhaust in an engine, steam in a turbine, and the air driven out of a mold during die casting must all be treated as compressible, because density changes control how mass and pressure move through them.[^barmeir-c1] ## History In 1887 Ernst Mach and Peter Salcher photographed a bullet in supersonic flight, "together with a thin layer of compressed air in front of it".[^guzzardi2023] The ratio of flow speed to sound speed was named the Mach number by Jakob Ackeret of ETH Zürich in 1929.[^hoi-mach] In the steam-turbine era Gustaf de Laval developed the converging–diverging nozzle, which he patented with a Belgian priority date of September 29, 1888.[^laval-patent] On October 14, 1947, Chuck Yeager flew the Bell X-1 to Mach 1.06, about 1,127 km/h, at 13,000 m over the Mojave Desert.[^nasm-x1] Genick Bar-Meir notes that the history of compressible flow as a separate discipline is much less documented than the history of hydraulics or of flight.[^barmeir-c1] ## Introductory concepts The central difference from incompressible flow is that pressure waves travel at a finite speed. In an incompressible model a push at one end of a pipe is felt instantly at the other; in a compressible fluid the news travels as a wave. Liquids show the effect too. Closing a valve very quickly on flowing water creates a pressure surge, or shock wave, in the pipe, the effect called water hammer.[^clemson] Because density and temperature now vary, [[Thermodynamics|thermodynamics]] joins the equations of motion, and [[Entropy|entropy]] decides which changes are possible.[^nasa-isentropic] ## Mach number, wave motion, and sonic speed The Mach number *M* is the flow speed divided by the local speed of sound. NASA's Glenn Research Center classifies flows as subsonic (*M* < 1), transonic (*M* ≈ 1), supersonic (1 < *M* < 3), high supersonic (3 < *M* < 5) and hypersonic (*M* > 5).[^nasa-mach] The Mach number controls how much density changes. In subsonic flow a rise in speed brings a smaller fall in density, but in supersonic flow density changes faster than velocity by a factor equal to *M*².[^nasa-role] ## One-dimensional flow ### Converging-diverging Laval nozzles In a converging–diverging nozzle, flow is subsonic upstream of the narrowest point, the throat, and can become supersonic downstream of it.[^nasa-nozzle] De Laval's patent describes the nozzle as "diverging or gradually enlarged in cross section from this narrowest point to its discharge opening."[^laval-patent] The result runs against everyday intuition: subsonic gas speeds up in a narrowing duct, but supersonic gas speeds up in a widening one. ### Isentropic flow Mach number relationships A flow without friction, heat transfer or shocks is isentropic, and its pressure, temperature and density can be written as functions of the Mach number alone. These relations hold as the speed approaches that of sound, but once shocks form they are no longer valid.[^nasa-isentropic] ### Non-isentropic 1D channel flow of a gas - normal shock waves A normal shock stands perpendicular to the flow. Across it the flow changes from supersonic to subsonic, and static pressure, temperature and density rise almost instantaneously. Total temperature stays the same, but total pressure always falls, which is the entropy cost of the shock.[^nasa-normal] Bar-Meir's text gives particular weight to internal flows in which wall friction (Fanno flow) or [[Heat_transfer|heat transfer]] (Rayleigh flow) drive a flow toward the choked, sonic state.[^barmeir-c1] Friction concentrates in the thin [[Boundary_layer|boundary layer]] along the walls, whose behavior depends on the [[Reynolds_number|Reynolds number]]. ## Two-dimensional flow ### Prandtl–Meyer fans When supersonic flow turns away from itself around a corner, it expands through a fan of weak waves. Through the fan the Mach number rises, static pressure falls and total pressure is unchanged, because the expansion is isentropic. The Prandtl–Meyer function gives the angle through which a sonic flow must turn to reach a given Mach number.[^nasa-fan] ## Applications ### Supersonic wind tunnels Supersonic wind tunnels use converging–diverging nozzles to accelerate air past a model. NASA Glenn's 10 × 10 Supersonic Wind Tunnel, which came online in 1956, runs its 10-by-10-by-40-foot test section at Mach 2.0 to 3.5.[^nasa-10x10] It tests supersonic propulsion components "from inlets and nozzles to full-scale jet and rocket engines," as well as large-scale models of [[Aircraft|aircraft]], and whole [[Jet_engine|jet engines]] can run in it.[^nasa-10x10] ## See also - [[Fluid_dynamics]] - [[Navier–Stokes_equations]] - [[Froude_number]], the open-channel analogue of the Mach number - [[Thermodynamics]] ## References [^britannica]: Encyclopaedia Britannica. "Compressible fluid flow." https://www.britannica.com/science/compressible-fluid-flow [^nasa-mach]: Hall, Nancy, ed. "Mach Number." Beginner's Guide to Aeronautics, NASA Glenn Research Center. https://www.grc.nasa.gov/www/k-12/airplane/mach.html [^nasa-role]: Hall, Nancy, ed. "Role of Mach Number in Compressible Flows." Beginner's Guide to Aeronautics, NASA Glenn Research Center. https://www.grc.nasa.gov/www/k-12/airplane/machrole.html [^nasa-isentropic]: Hall, Nancy, ed. "Isentropic Flow Equations." Beginner's Guide to Aeronautics, NASA Glenn Research Center. https://www.grc.nasa.gov/www/k-12/airplane/isentrop.html [^nasa-normal]: Hall, Nancy, ed. "Normal Shock Wave Equations." Beginner's Guide to Aeronautics, NASA Glenn Research Center. https://www.grc.nasa.gov/www/k-12/airplane/normal.html [^nasa-nozzle]: Hall, Nancy, ed. "Nozzles." Beginner's Guide to Aeronautics, NASA Glenn Research Center. https://www.grc.nasa.gov/www/k-12/airplane/nozzle.html [^nasa-fan]: Hall, Nancy, ed. "Centered Expansion Fan." Beginner's Guide to Aeronautics, NASA Glenn Research Center. https://www.grc.nasa.gov/www/K-12/airplane/expans.html [^nasa-10x10]: NASA. "10×10 Supersonic Wind Tunnel." Glenn Research Center. https://www.nasa.gov/centers-and-facilities/glenn/10x10-supersonic-wind-tunnel/ [^laval-patent]: de Laval, Carl Gustaf Patrik. "Steam Turbine." U.S. Patent 522,066, filed May 1, 1889, granted June 26, 1894 (Belgian priority September 29, 1888). https://patents.google.com/patent/US522066A/en [^guzzardi2023]: Guzzardi, Luca (2023). "Epistemology in practice: Ernst Mach's experiments on shock waves and the place of philosophy." *Journal for General Philosophy of Science* 54 (1): 79–98. https://doi.org/10.1007/s10838-022-09602-9 [^hoi-mach]: "Mach and Salcher photograph supersonic shock waves." HistoryofInformation.com. https://www.historyofinformation.com/detail.php?id=3262 [^nasm-x1]: Smithsonian National Air and Space Museum. "Bell X-1 *Glamorous Glennis*." https://airandspace.si.edu/collection-objects/bell-x-1-glamorous-glennis/nasm_A19510007000 [^clemson]: Smith, W. B. (2019). "Homemade Hydraulic Ram Pump for Livestock Water." Clemson University Land-Grant Press, LGP 1017. https://lgpress.clemson.edu/publication/homemade-hydraulic-ram-pump-for-livestock-water/ [^barmeir-c1]: Bar-Meir, Genick (2026). *Fundamentals of Compressible Flow Mechanics*, version 0.5.4. Chapter 1, §1.2 "Why Compressible Flow is Important?" and §1.3 "Historical Background." https://zenodo.org/records/18217916 ## External links - [Beginner's Guide to Aeronautics](https://www.grc.nasa.gov/www/k-12/airplane/), NASA Glenn Research Center - Bar-Meir, *Fundamentals of Compressible Flow Mechanics* — on the [[PORTAL_WT!Thury_Hydrodynamics_Compendium|Compendium]] Fluid core and Transportation shelves and the [[PORTAL_Aviation]] shelf  **Part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]]** — main article for section 25, *When water hits hard*. Related sections: [[Hydroelectricity]] · [[Hydraulic_jump]] · [[Hydraulic_ram]].   **Microsim — three.js (Wikitube framework):** *Compressible flow* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Compressible_flow.html" data-title="Compressible flow"></div> *Built from `MICROSIM_GUIDE/specs/sims/Compressible_flow.json`; part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]] set.*   *Linked from the [[Aviation]] hub, section A11, Faster than sound.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Compressible_flow) : [Wikitube](https://en.wikitube.io/wiki/Compressible_flow) · pinned revision [1373989359](https://en.wikipedia.org/w/index.php?oldid=1373989359) · 2026-09-10 ## Previous hub tags Hubs: `Life_Physics`, `Systems`. Portals: [[PORTAL_Thury_Hydrodynamics_Apex_Spine]], [[PORTAL_Aviation]]. --- *Thury main articles, wave 2 · 2026-09-10 · drafted · Compendium section 25 · sim pending THY-030.*