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We take a top-down approach of formulating the rate control problem, over a collection tree, in a wireless sensor network as a generic convex optimization problem and propose a distributed back pressure algorithm using Lyapunov drift based optimization techniques. Primarily, we show that existing theoretical results in the field of stochastic network optimization can be directly applied to a CSMA based wireless sensor network using our novel receiver capacity model. We back this claim by implementing our algorithm on the Tmote sky class devices. Our experimental evaluation on a 5 node testbed shows that the empirically observed rate allocation on a real sensor network testbed that uses our back pressure algorithm is close to the analytically predicted values, justifying our claims.