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By: Justin

The weight of the parcel is $\mathrm {V} \mathbf {g}$ , while the pressure gradient force is ${\frac {dp}{dz}}$ . Using the hydrostatic assumption (both terms equal zero) and observing that $\rho V{\frac {dw}{dt}}=0$ in this case gives $\rho V{\frac {dw}{dt}}=-V{\frac {dp}{dz}}-V\rho g$ Allowing for the pressure to be the sum of the environmental and parcel pressure $p={\bar {p}}+p^{\prime }$ yields the following as the buoyancy equation: ${\frac {dw}{dt}}=-{\frac {1}{\rho }}{\frac {dp^{\prime }}{dz}}+{\frac {{\bar {\rho }}-\rho }{\rho }}$ . From the second equation it is easily seen that if the parcel is denser than its environment(i.e. $p>{\bar {p}}$ , it will have a negative buoyancy and will thus sink relative to the environment. The opposite case is also true ( $p<{\bar {p}}$ causes rising), while neutral buoyancy is achieved by the two terms being equal.

FBI

It can own CIA every day, if you agree, BAH! However if you don't I will eat your soul in real life, oh I forgot I can't, because I'm no demon, I'm a human.