The launch of Hinode satellite led to the discovery of rising plumes , dark in chromospheric lines , in quiescent prominences that propagate from large ( \sim 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 \pm 0.079 to 1.13 \pm 0.080 for the range \gamma = 1.4 - 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 .