ABSTRACT
If we consider the left-hand sides of these equalities as Cartesian components of a vector, we obtain Z
grad p dV =
Z
p(n) d; (C.8)
since n =< n; i > i+ < n; j > j+ < n;k > k: (C.9)
As a matter of general interest, note that we can immediately obtain Archimedes' buoyancy principle for a body totally immersed in a liquid with constant density , in which case, grad p = g, so that the buoyancy force reads
F() = Z
p(nd) =
Z
g dV = g
Z
dV = gM =W; (C.10)
where W is the weight of the displaced mass of uid.
