
Mass Flow Rate

Glenn Research Center

The conservation of mass is a fundamental
concept of physics. Within some problem domain, the amount of mass
remains constant mass is neither created nor destroyed. The
mass of any object is simply the volume that the object
occupies times the density of the object.
For a fluid (a liquid or a gas) the
density, volume, and shape of the object can all change within the
domain with time. And mass can move through the domain. On the
figure, we show a flow of gas through a constricted tube. There is no
accumulation or destruction of mass through the tube; the same amount
of mass leaves the tube as enters the tube. At any plane
perpendicular to the center line of the tube, the same amount of mass
passes through. We call the amount of mass passing through a plane
the mass flow rate. The conservation of mass
(continuity) tells us that the mass flow rate through a tube is a
constant. We can determine the value of the mass flow rate from the
flow conditions.
If the fluid initially passes through an area A at velocity V,
we can define a volume of mass to be swept out in some amount of time
t. The volume v is:
v = A * V * t
A units check gives area x
length/time x time = area x length = volume. The mass m contained in
this volume is simply density r times the volume.
m = r * A * V * t
To determine the mass flow rate mdot, we divide
the mass by the time. The resulting definition of mass flow rate is
shown on the slide in red.
mdot = r * A * V
How do engineers use this knowledge of the mass flow rate? From
Newton's Second Law of Motion, the
aerodynamic forces on an aircraft (lift
and drag) are directly related to the change
in momentum of a gas with time. The
momentum is defined to be the mass times the velocity, so we
would expect the aerodynamic forces to depend on the mass flow rate
past an object. The thrust produced by a
propulsion system also depends on the change
of momentum of a working gas. The thrust depends directly on the mass
flow rate through the propulsion system. For flow in a tube, the mass
flow rate is a constant. For a constant density flow, if we can
determine (or set) the velocity at some known area, the
equation tells us the value of velocity for any other area. If we
desire a certain velocity, we know the area we have to provide to
obtain that velocity. This information is used in the design of
wind tunnels.
Considering the mass flow rate equation, it would appear that for
a given area, we could make the mass flow rate as large as we want by
setting the velocity very high. However, in real fluids, compressibility
effects limit the speed at which a flow can be forced through a
given area. If there is a slight constriction in the tube, as shown
in the nozzle graphics, the Mach number of
the flow through the constriction cannot be greater than one. This is
commonly referred to as flow choking and the details
of the physics are given on a page considering compressible
mass flow rates.
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