Bernoulli equation
E173920
The Bernoulli equation is a fundamental principle in fluid dynamics that relates pressure, velocity, and elevation in steady, incompressible, inviscid flow along a streamline.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Bernoulli principle | 3 |
| Bernoulli's principle | 2 |
| Bernoulli equation canonical | 1 |
| Bernoulli theorem | 1 |
| Bernoulli's principle in fluid dynamics | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1523253 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bernoulli equation Context triple: [Euler equations, relatedTo, Bernoulli equation]
-
A.
Pascal's law
Pascal's law is a fundamental principle of fluid mechanics stating that pressure applied to an enclosed fluid is transmitted undiminished in all directions throughout the fluid and to the walls of its container.
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B.
Bernoulli
Bernoulli is the surname of a prominent Swiss family of mathematicians and scientists, including figures such as Jakob, Johann, and Daniel Bernoulli, who made foundational contributions to calculus, probability, and fluid dynamics.
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C.
Euler equations
The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.
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D.
Navier–Stokes equations
The Navier–Stokes equations are fundamental partial differential equations in fluid mechanics that describe how the velocity field of a fluid evolves under forces like pressure and viscosity.
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E.
Stokes' law
Stokes' law is a fundamental equation in fluid dynamics that describes the drag force experienced by small spherical particles moving slowly through a viscous fluid.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bernoulli equation Target entity description: The Bernoulli equation is a fundamental principle in fluid dynamics that relates pressure, velocity, and elevation in steady, incompressible, inviscid flow along a streamline.
-
A.
Pascal's law
Pascal's law is a fundamental principle of fluid mechanics stating that pressure applied to an enclosed fluid is transmitted undiminished in all directions throughout the fluid and to the walls of its container.
-
B.
Bernoulli
Bernoulli is the surname of a prominent Swiss family of mathematicians and scientists, including figures such as Jakob, Johann, and Daniel Bernoulli, who made foundational contributions to calculus, probability, and fluid dynamics.
-
C.
Euler equations
The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.
-
D.
Navier–Stokes equations
The Navier–Stokes equations are fundamental partial differential equations in fluid mechanics that describe how the velocity field of a fluid evolves under forces like pressure and viscosity.
-
E.
Stokes' law
Stokes' law is a fundamental equation in fluid dynamics that describes the drag force experienced by small spherical particles moving slowly through a viscous fluid.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
equation in fluid dynamics
ⓘ
physical law ⓘ |
| appliesTo |
flow along a streamline
ⓘ
incompressible flow ⓘ inviscid flow ⓘ steady flow ⓘ |
| assumes |
constant density
ⓘ
no shaft work along the streamline ⓘ no significant heat transfer along the streamline ⓘ no viscous dissipation ⓘ |
| category |
conservation laws in physics
ⓘ
equations of fluid mechanics ⓘ |
| coordinateSystem | streamline coordinates ⓘ |
| describes | conversion between pressure energy, kinetic energy, and potential energy in a fluid ⓘ |
| expressesConservationOf | mechanical energy per unit volume ⓘ |
| field |
fluid dynamics
ⓘ
hydrodynamics ⓘ |
| generalization | energy equation for real fluids ⓘ |
| hasForm | p + 1/2 ρ v^2 + ρ g z = constant ⓘ |
| hasFormVariant | p/γ + v^2/(2g) + z = constant ⓘ |
| isBasisFor |
Bernoulli equation
self-linksurface differs
ⓘ
surface form:
Bernoulli principle
Bernoulli’s theorem in engineering practice ⓘ |
| limitation |
not valid across shock waves
ⓘ
not valid for highly viscous flows ⓘ not valid for strongly compressible high-speed flows without modification ⓘ |
| namedAfter | Daniel Bernoulli ⓘ |
| publication | Hydrodynamica ⓘ |
| publicationYear | 1738 ⓘ |
| relatedConcept |
Euler equations
ⓘ
surface form:
Euler equations of fluid motion
Navier–Stokes equations ⓘ continuity equation in fluid mechanics ⓘ |
| relates |
elevation
ⓘ
flow velocity ⓘ pressure ⓘ |
| term |
elevation head
ⓘ
pressure head ⓘ velocity head ⓘ |
| usedFor |
Pitot tube analysis
ⓘ
Venturi meter analysis ⓘ aerodynamic lift estimation ⓘ flow measurement ⓘ open-channel flow approximations ⓘ orifice meter analysis ⓘ pipe flow analysis ⓘ |
| variable |
g
ⓘ
p ⓘ v ⓘ z ⓘ ρ ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Bernoulli equation Description of subject: The Bernoulli equation is a fundamental principle in fluid dynamics that relates pressure, velocity, and elevation in steady, incompressible, inviscid flow along a streamline.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Daniel Bernoulli
this entity surface form:
Bernoulli principle
this entity surface form:
Bernoulli principle
this entity surface form:
Bernoulli theorem
this entity surface form:
Bernoulli principle
this entity surface form:
Bernoulli's principle
this entity surface form:
Bernoulli's principle in fluid dynamics
this entity surface form:
Bernoulli's principle