Mass flow rate boundary condition for continuity equation for oscillating flow
 

I am doing numerical coding for oscillating flow in a pulse tube cryocooler. In which my continuity is of the following form:
dm/dt = mf(in)-mf(out)

Where dm/dt is change in mass, mf is mass flow rate, kg/s

Also I am simulating pipe as 1-D domain. Flow is entering during pressurization by compressor and reversed during depressurization. This mass flow rate during pressurization and depressurization is obtained by nozzle equation at the one end of pipe. But at the second end, pipe is closed in first case and in second case pipe is oped to reservoir via orifice valve (governed by nozzle equation).

Now I want to know what should be the Boundary conditions (B.C) for both the case.
1st case:
I have taken left BC as nozzle mass flow rate at first face i.e. left face of pipe and at last face of pipe i.e. open means mf is zero. Now can you tell me what should be the BC in second case?