Opening your learning space
Starting the app …
Opening your learning space
Starting the app …
The Froude number compares inertia with gravity effects and governs dynamic similarity in free-surface flows.
Free to browse · flashcards or a multiple-choice quiz · import from Essential
Formula
Fr dimensionless; U in m/s; g in m/s2; L in m
| Symbol | Meaning | Unit |
|---|---|---|
| Froude number for the chosen characteristic scale | dimensionless | |
| Characteristic velocity | m/s | |
| Gravitational acceleration | m/s2 | |
| Characteristic length such as waterline length | m |
Fr=\frac{U}{\sqrt{gL}}This entry uses the unsquared convention Fr=U/√(gL); some sources report Fr2. It is especially relevant to free surfaces and gravity waves and depends on the selected length scale. Matching Fr between model and prototype supports dynamic similarity but does not also guarantee matching Reynolds number, roughness or every boundary condition.
This entry uses the unsquared convention Fr=U/√(gL); some sources report Fr2. It is especially relevant to free surfaces and gravity waves and depends on the selected length scale. Matching Fr between model and prototype supports dynamic similarity but does not also guarantee matching Reynolds number, roughness or every boundary condition.
The Froude number compares inertia with gravity effects and governs dynamic similarity in free-surface flows.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Froude number” and check its unit and magnitude.
A model hull moving at U=2.0 m/s with waterline length L=1.0 m has Fr=2/√(9.81·1)=0.639.
A Froude-similar prototype should match this value.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: Fr dimensionless; U in m/s; g in m/s2; L in m.
Formula cluster
The Froude number compares inertia with gravity effects and governs dynamic similarity in free-surface flows.
A model hull moving at U=2.0 m/s with waterline length L=1.0 m has Fr=2/√(9.81·1)=0.639. A Froude-similar prototype should match this value.
Scale ship models, channels, weirs and other free-surface flows.
Here is how to work through a typical Froude number (Fr = U/√(gL)) task step by step:
Task
Work through the numerical example for “Froude number” and check its unit and magnitude.
Solution path
A model hull moving at U=2.0 m/s with waterline length L=1.0 m has Fr=2/√(9.81·1)=0.639.
A Froude-similar prototype should match this value.
gL has units (m/s2)·m=m2/s2. Its square root is m/s, so it can be compared with U. Dimensional analysis checks the formula. A different characteristic length keeps Fr dimensionless but changes the physical comparison. This entry uses Fr=U/√(gL); the characteristic length and free surface must fit the application. Application: Scale ship models, channels, weirs and other free-surface flows. The numerical example A model hull moving at U=2.0 m/s with waterline length L=1.0 m has Fr=2/√(9.81·1)=0.639. A Froude-similar prototype should match this value anchors the idea in a concrete measurement case.
In free-surface problems, inertia and gravity matter strongly, such as ship waves or open-channel flow. A geometric model often needs the same Fr as the prototype. Because of scale changes, Reynolds number may not also match exactly; experiments must prioritize the dominant effects. This entry uses Fr=U/√(gL); the characteristic length and free surface must fit the application. The corresponding units are Fr dimensionless; U in m/s; g in m/s2; L in m. A model hull moving at U=2.0 m/s with waterline length L=1.0 m has Fr=2/√(9.81·1)=0.639. A Froude-similar prototype should match this value. This checks that the reference quantities are compatible.
Fr captures only the ratio of inertia and gravity. Viscosity, surface tension, roughness and boundary conditions may also matter. In small models, viscous or capillary effects can become relatively more important. State geometry, length scale and other governing groups before transferring measurements. This entry uses Fr=U/√(gL); the characteristic length and free surface must fit the application. Scope: This entry uses the unsquared convention Fr=U/√(gL); some sources report Fr2. It is especially relevant to free surfaces and gravity waves and depends on the selected length scale. Matching Fr between model and prototype supports dynamic similarity but does not also guarantee matching Reynolds number, roughness or every boundary condition. A practical application is Scale ship models, channels, weirs and other free-surface flows.
Write the quantity and unit from the variable list next to every value: Fr dimensionless; U in m/s; g in m/s2; L in m. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example A model hull moving at U=2.0 m/s with waterline length L=1.0 m has Fr=2/√(9.81·1)=0.639. A Froude-similar prototype should match this value. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. This entry uses Fr=U/√(gL); the characteristic length and free surface must fit the application.
The background states this starting condition: This entry uses the unsquared convention Fr=U/√(gL); some sources report Fr2. It is especially relevant to free surfaces. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. This entry uses Fr=U/√(gL); the characteristic length and free surface must fit the application.
Quanta exam set
Curated exam set for "Froude number":
Question (front)
Which formula describes Froude number?
Answer in your set
Question (front)
How do you rearrange Froude number for Base equation for the target quantity?
Answer in your set
Question (front)
Which common mistake happens with Froude number?
Answer in your set
+ 7 more cards: units, variables, derivation, example, exam task
The formula set contains 10 cards. After importing, review them and start practicing; your ratings determine later review intervals.
This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.
Create a curated FSRS exam set for Fr = U/√(gL): formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.
Curated formula set · LaTeX · FSRS spaced repetition · import from Essential