The mass flow rate () is defined as the amount of mass flowing through a cross-section per unit time. The mass flow rate of a fluid flowing in or out of a pipe or duct is proportional to the cross-sectional area (A) of the pipe or duct, the density of the fluid (ρ), and the velocity of the flow (V). The flow rate through a differential area dA is:

      d = ρV_ndA

where
      V_n = the velocity component normal to the area dA

Normal Velocity Component

Integrating the above equation to get the total mass flow rate.

The volume flow rate () is the volume of the fluid flowing through a cross-sectional area per unit time.

      

The mass and volume flow rate are related by

System Used for
Conservation of Mass Equation

The conservation of mass principle states the following:

In an equation format, the conservation of mass principle is:

(Total mass entering the system)
  -
(Total mass leaving the system)
 =
(Net change in mass within the system)

or,

      m_in - m_out = Δm_system

where
      Δm_system = m_system@final - m_{system@initial}

The rate form of the conservation of mass principle is:

(Rate at which mass entering the system)
-
(Rate at which mass leaving the system)
=
(time rate of change in mass within the system)

or,
      

Mass Remains Constant for a
Closed System

A closed system is defined as a system which mass can not cross its boundaries, but energy transfer is allowed. Since no mass flows in or out of the system, the mass of the closed system remains constant during a process.