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z=gc6Cv{PD4W+^H(cdKz>Z>`~1=jXKJdc~uPFbI7Vut778>Oo06WvLT5cA2f6%LyS* z({$+~wv9>SWzh1Ha-8GEGZSA&N|JU}V)#`i>(|Y<(^x%qRB*3 R+4}$h002ovPDHLkV1oH>ks<&9 literal 0 HcmV?d00001 diff --git a/mechanical/mmme1048_fluid_mechanics.md b/mechanical/mmme1048_fluid_mechanics.md index 0eba855..5eb4f1b 100755 --- a/mechanical/mmme1048_fluid_mechanics.md +++ b/mechanical/mmme1048_fluid_mechanics.md @@ -466,3 +466,41 @@ M_{OO} &= F_py_p = \int_{area}\! \rho gh^2 \,\mathrm{d}A \\ \\ y_p = \frac{M_{OO}}{F_p} \end{align*} + +## Buoyancy + +### Archimedes Principle + +> The resultant upwards force (buoyancy force) on a body wholly or partially immersed in a fluid is +> equal to the weight of the displaced fluid. + +When an object is in equilibrium the forces acting on it balance. +For a floating object, the upwards force equals the weight: + +$$mg = \rho Vg$$ + +Where $\rho$ is the density of the fluid, and $V$ is the volume of displaced fluid. + +### Immersed Bodies + +As pressure increases with depth, the fluid exerts a resultant upward force on a body. +There is no horizontal component of the buoyancy force because the vertiscal projection of the body +is the same in both directions. + +### Rise, Sink, or Float? + +- $F_B = W$ \rightarrow equilirbrium (floating) +- $F_B > W$ \rightarrow body rises +- $F_B < W$ \rightarrow body sinks + +### Centre of Buoyancy + +Buoyancy force acts through the centre of gravity of the volume of fluid displaced. +This is known as the centre of buoyancy. +The centre of buoyancy does not in general correspond to the centre of gravity of the body. + +If the fluid density is constant the centre of gravity of the displaced fluid is at the centroid of +the immersed volume. + +![](./images/vimscrot-2021-12-21T15:08:22,285753421+00:00.png) +