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In [[fluid dynamics]], the '''Froude–Krylov force'''—sometimes also called the '''Froude–Kriloff force'''—is a [[hydrodynamics|hydrodynamical]] [[force]] named after [[William Froude]] and [[Alexei Krylov]]. The Froude–Krylov force is the force introduced by the unsteady [[pressure]] [[Field (physics)|field]] generated by ''undisturbed'' [[Ocean surface wave|waves]]. The Froude–Krylov force does, together with the [[diffraction]] force, make up the total non-[[viscous]] forces acting on a floating body in regular waves. The diffraction force is due to the floating body disturbing the waves.

== Formulas ==

The Froude–Krylov force can be calculated from:

:<math>
 \vec F_{FK} = - \iint_{S_w} p ~ \vec n ~ ds,
</math>

where
*<math>\vec F_{FK}</math> is the Froude–Krylov force,
*<math>S_w</math> is the wetted surface of the floating body,
*<math>p</math> is the pressure in the undisturbed waves and
*<math>\vec n</math> the body's [[surface normal|normal vector]] pointing into the water.

In the simplest case the formula may be expressed as the product of the wetted surface area (A) of the floating body, and the dynamic pressure acting from the waves on the body:

:<math>
F_{FK} = A \cdot p_{dyn} 
</math>

The dynamic pressure, <math>p_{dyn}</math>, close to the surface, is given by:

:<math>
p_{dyn} = \rho \cdot g \cdot H/2
</math>

where
*<math>\rho</math> is the [[Properties of water#Density of saltwater and ice|sea water density]] (approx. 1030&nbsp;kg/m³)
*<math>g</math> is the [[standard gravity|acceleration due to the earth's gravity]] (9.81&nbsp;m/s²)
*<math>H</math> is the wave height from [[Crest (physics)|crest]] to [[trough (physics)|trough]].

== See also ==
* [[Response amplitude operator|Response Amplitude Operator]]

== References ==
* {{cite book
  | last = Faltinsen
  | first = O. M.
  | title = Sea Loads on Ships and Offshore Structures
  | publisher = [[Cambridge University Press]]
  | year = 1990
  | isbn = 978-0-521-45870-2 }}

{{DEFAULTSORT:Froude-Krylov force}}
[[Category:Shipbuilding]]
[[Category:Naval architecture]]
[[Category:Fluid dynamics]]


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