In a closed circulation system, when the rig pumps are on, the fundamental pressure equation is
BHPdynamic = Pstatic + Pafp + Pbp
where Pstatic and Pafp are static and annular frictional pressure respectivel, and Pbp is the surface backpressure applied to the annulus by pressure control equipment connected to the wellhead.
This equation applies when the rig mud pumps are on and mud is circulating.
Under static conditions when the rig pumps are off Pafp = 0 and BHPdynamic becomes
BHPstatic = Pstatic + Pbp
In a closed system the backpressure term, Pbp, is always present during a connection and depending on the MPD application, while drilling, during tripping, even during unpanned stoppages for rig repairs.
It is through control of the backpressure that the BHP can be maintained at a constant value from dynamic to static conditions, i.e. from pumps-on to pumps-off without raising the static mud weight.
However, not all constant bottomhole pressure applications require dynamic and static BHP to be equal just as long as they are both within the specified safe operating limits.