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I have a question regarding a pipe-network:

enter image description here

Pressure A > B
diameters of the outside pipes are bigger than the pipe with the massflow m2,m3

The brown rectangle is a valve (the diameter of the valve is smaller than the pipe-diameter). I know from the continuity equation, that the volume flow rate in a pipe is constant. But how is that relation within a network? Is:

massflow: m2 < m3(through the valve)?
massflow m1 < m2 (smaller diameter)?
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Actually the continuity equation means that at steady state, the mass flowrate in a pipe must be constant (as mass cannot be created or destroyed not volume) but the volume can vary.
so:

m2=m3

If this fluid is incompressible such (as water) the volume flowrate would be the same, but for a compressible fluid such as a gas the volumetric flowrate at point 3 would be higher than point 2. (the pressure drop would lead to an expansion of the gas)

The pressure drop in both branches must be the same. Pressure drop is proportional to velocity so you need more volume in a larger cross-sectional area pipe to produce the same velocity (velocity = volumetric flowrate / cross sectional area). The valve will act as an obstruction resulting in even more pressure drop for a given velocity. Therefore you need much more fluid to travel through the large diameter, unobstructed branch so

m1>m2
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