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I would like to know if I can apply the conservation of momentum to the rate of change of pressure at a fixed position (for e.g. x=0) as follows:

dP1/dt=-dP2/dt

where dP1 is the pressure changes over a fixed interval of time (del t1) and dP2 is the pressure changes over another fixed interval of time (del t2) at x=0, and del t1 = del t2.

Can I explain the above equation as follows:

at x=0, pressure increases by dP1 in del t1 and this dP1/dt is balanced by an equivalent negative rate of momentum changing force per unit area, -dP2/dt after certain period of time.

Thank you very much for your kind assistance.

Sarah