Definition
Mass flow rate is defined by the limit:
i.e. the flow of mass m through a surface per unit time t.
The overdot on the m is Newton's notation for a time derivative. Since mass is a scalar quantity, the mass flow rate (the time derivative of mass) is also a scalar quantity. The change in mass is the amount that flows after crossing the boundary for some time duration, not simply the initial amount of mass at the boundary minus the final amount at the boundary, since the change in mass flowing through the area would be zero for steady flow.
Read more about this topic: Mass Flow Rate
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