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De Laval Nozzle

A converging–diverging nozzle that chokes compressible flow at its throat and accelerates it supersonically in the divergent section under suitable pressure ratio.

Version
v1 · 2026-09-28 · History
Domain-specific #
8870
Domain group
Applied Sciences & Engineering
Origin domain
Engineering & Design (beyond software)
Subdomains
Compressible Flow, Nozzle Design → Engineering & Design (beyond software)
Aliases
Convergent-divergent nozzle, Converging-diverging nozzle, CD nozzle

Core Idea

A de Laval nozzle is a converging throat followed by a diverging passage that, under sufficient pressure ratio, chokes a compressible flow at the throat and accelerates it to supersonic speed downstream by converting enthalpy to directed kinetic energy.

High reservoir pressure drives gas to Mach one at the throat and to supersonic speed through the divergent exit. Raised back pressure produces a normal shock in the diverging passage, losing the intended smooth expansion.

How would you explain it like I'm…

The Hourglass Speed Tube

A de Laval nozzle is a tube that gets skinny in the middle and then wider again, like an hourglass. When gas is pushed hard enough through it, it squeezes through the skinny part as fast as sound, and then the widening part makes it go even faster, faster than sound. Rockets use this shape to shoot their hot gas out super fast.

The Squeeze-Then-Spread Nozzle

A de Laval nozzle is a tube that narrows to a tight neck, called the throat, and then gets wider again. When gas is pushed in at high pressure, it speeds up as the tube narrows and reaches the speed of sound right at the throat. After that, in the widening part, the fast gas actually speeds up even more, going faster than sound, while its heat and pressure turn into forward motion. This only works if the pressure going in is high enough compared to the pressure outside. If the outside pressure is too high, a sudden shock wave forms inside the wide part and ruins the smooth speed-up.

Converging-Diverging Supersonic Nozzle

A de Laval nozzle has a converging section that narrows to a throat, followed by a diverging section that widens. For gases, which compress, this shape behaves in a surprising way. If the pressure ratio between the gas supply and the outside is large enough, the flow reaches Mach 1, the speed of sound, at the throat, and the flow is said to be choked there. In the diverging section the gas then keeps expanding and accelerates to supersonic speed, converting its thermal energy (enthalpy) into directed kinetic energy. If the back pressure at the exit is raised too much, a normal shock wave forms in the diverging part and the intended smooth supersonic expansion is lost.

 

A de Laval nozzle is a converging-diverging duct used to accelerate compressible flow to supersonic speed. With a sufficiently high ratio of reservoir pressure to back pressure, the flow accelerates through the converging section to Mach 1 at the throat, where it chokes, fixing the mass flow rate. Downstream, in the diverging passage, the supersonic flow continues to expand and accelerate, converting enthalpy into directed kinetic energy, which is why such nozzles are central to rocket engines and supersonic flows. The behavior reverses the subsonic intuition that a widening duct slows flow: past Mach 1, area increase accelerates the gas. If the back pressure is raised above the design condition, a normal shock stands in the diverging section, after which the flow becomes subsonic and the intended smooth expansion is lost. Operation therefore depends on the pressure ratio, not on geometry alone.

Structural Signature

Sig role-phrases:

  • Reservoir state — Supplies stagnation pressure and temperature. It is input. Counterfactual: Insufficient pressure ratio prevents intended regime.
  • Converging section — Accelerates subsonic flow toward the throat. It is geometry. Counterfactual: Divergence alone does not establish choking.
  • Minimum-area throat — Reaches Mach one when choked. It is critical section. Counterfactual: A noncritical throat changes mass-flow control.
  • Diverging section — Accelerates already supersonic flow as area increases. It is expansion. Counterfactual: Subsonic flow would decelerate there.
  • Back pressure — Selects shock, separation, or design expansion regime. It is boundary condition. Counterfactual: Geometry alone cannot guarantee clean supersonic exhaust.
  • Energy conversion — Trades enthalpy and pressure for axial velocity. It is function. Counterfactual: Losses reduce realized performance.

What It Is Not

  • It is not every narrowed pipe.
  • It is not a Venturi meter by default.
  • It is not guaranteed supersonic by shape alone.
  • It is not an incompressible diffuser.
  • Closest near-miss. A Venturi has similar geometry but normally measures subsonic pressure change rather than sustaining supersonic expansion.

Scope of Application

  • Rocket propulsion. Accelerates exhaust.
  • Steam turbines. Produces high-speed jets.
  • Supersonic tunnels. Sets test-section flow.
  • Astrophysics. Provides an analogy for accelerating compressible outflows.

Clarity

Include converging–throat–diverging ducts operating with compressible flow and conditions capable of choking and downstream supersonic expansion. Exclude Venturi meters operated subsonically, simple converging nozzles, incompressible diffusers, and hourglass shapes with no qualifying pressure regime.

Manages Complexity

The throat fixes maximum mass flow while area ratio and back pressure set exit state. Isentropic analysis clarifies geometry but viscosity, shocks, and separation reduce performance.

Abstract Reasoning

  1. Reservoir state — Supplies stagnation pressure and temperature. Insufficient pressure ratio prevents intended regime.
  2. Converging section — Accelerates subsonic flow toward the throat. Divergence alone does not establish choking.
  3. Minimum-area throat — Reaches Mach one when choked. A noncritical throat changes mass-flow control.
  4. Diverging section — Accelerates already supersonic flow as area increases. Subsonic flow would decelerate there.
  5. Back pressure — Selects shock, separation, or design expansion regime. Geometry alone cannot guarantee clean supersonic exhaust.
  6. Energy conversion — Trades enthalpy and pressure for axial velocity. Losses reduce realized performance.

Knowledge Transfer

Area–Mach reasoning transfers to compressible gas passages with a known equation of state and boundary pressures; an hourglass geometry in incompressible flow does not inherit choking or supersonic expansion.

Examples

Applied / In Practice

High reservoir pressure drives gas to Mach one at the throat and to supersonic speed through the divergent exit.

Mapped back: inlet → stagnation state; throat → choked; exit → supersonic.

Applied / In Practice

Raised back pressure produces a normal shock in the diverging passage, losing the intended smooth expansion.

Mapped back: condition → high back pressure; event → shock.

Structural Tensions

T1 — Mass-Flow Choking versus Exit Matching. The throat fixes maximum mass flow while area ratio and back pressure set exit state.

Diagnostic: Is the nozzle on design?

T2 — Ideal Expansion versus Real Losses. Isentropic analysis clarifies geometry but viscosity, shocks, and separation reduce performance.

Diagnostic: Which losses are included?

Structural–Framed Character

Supplies stagnation pressure and temperature. Accelerates subsonic flow toward the throat. The throat fixes maximum mass flow while area ratio and back pressure set exit state.

Structural Core vs. Domain Accent

Selects shock, separation, or design expansion regime. Trades enthalpy and pressure for axial velocity. The defining operation exits when flow is unchoked or remains subsonic through the divergent section.

  • Approved root. The frozen graph retains de Laval nozzle without a parent edge.

  • Related — Venturi tube and Converging nozzle. Typically remains subsonic and measures flow. Can choke but lacks downstream expansion.

Neighborhood in Abstraction Space

De Laval Nozzle sits in a crowded region of the domain-specific corpus (36th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Thermodynamic & Transport Processes (34 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With

  • Venturi tube. Tell: Typically remains subsonic and measures flow.
  • Converging nozzle. Tell: Can choke but lacks downstream expansion.
  • Diffuser. Tell: Usually decelerates flow.
  • Orifice. Tell: A thin restriction without controlled area distribution.

References

  • Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/De_Laval_nozzle (revision 1369805434).
  • Preserved source candidate: https://archive.org/details/principlesastrop00clar_804
  • Preserved source candidate: https://archive.org/details/principlesastrop00clar_804/page/n237
  • Preserved source candidate: https://books.google.com/books?id=PmuqCHDC3pwC&q=nozzle+Ernst+Koerting&pg=PA396
  • Preserved source candidate: https://web.archive.org/web/20210910180759/https://books.google.com/books?id=PmuqCHDC3pwC&q=nozzle+Ernst+Koerting&pg=PA396
  • Preserved source candidate: http://pdfpiw.uspto.gov/.piw?docid=00522066&PageNum=1&IDKey=881F85454D87
  • Preserved source candidate: https://web.archive.org/web/20180111165305/http://pdfpiw.uspto.gov/.piw?docid=00522066&PageNum=1&IDKey=881F85454D87
  • Preserved source candidate: https://books.google.com/books?id=9ElMAAAAMAAJ&pg=PA27
  • Preserved source candidate: https://web.archive.org/web/20141019162649/http://books.google.com/books?id=9ElMAAAAMAAJ&pg=PA27&lpg=PA26&ots=i9N3YYNjIF&ie=ISO-8859-1&output=html

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.