Mass and Volume Flow Rate

Mass Flow Rate Through a Duct

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 = ρVndA

      Vn = 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


    Conservation of Mass Principle

System Used for
Conservation of Mass Equation


The conservation of mass principle states the following:

Net mass transfer to or from a system during a process is equal to the net change in the total mass of the system during that process.

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)


Filling and Emptying Bathtub is an
Example of Mass Conservation


      min - mout = Δmsystem

      Δmsystem = msystem@final - msystem@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)


  Conservation of Mass for Closed System

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.