  The launch of Hinode satellite led to the discovery of rising plumes, dark in
chromospheric lines, in quiescent prominences that propagate from large (~10
Mm) bubbles that form at the base of the prominences. These plumes present a
very interesting opportunity to study Magnetohydrodynamic (MHD) phenomena in
quiescent prominences, but obstacles still remain. One of the biggest issues is
that of the magnetic field strength, which is not easily measurable in
prominences. In this paper we present a method that may be used to determine a
prominence's plasma \beta when rising plumes are observed. Using the classic
fluid dynamic solution for flow around a circular cylinder with an MHD
correction, the compression of the prominence material can be estimated. This
has been successfully confirmed through simulations; application to a
prominence gave an estimate of the plasma beta as \beta=0.47 to 1.13 with an
error of 0.080 for the range \gamma=1.4 to 1.7. Using this method it may be
possible to estimate the plasma beta of observed prominences, therefore helping
our understanding of a prominence's dynamics in terms of MHD phenomena.
