CONTINUITY EQUATION
Fluid Flow
Replacing
in Equation 3-2 with the appropriate terms from Equation 3-1 allows the direct
V
calculation of the mass flow rate.
(3-3)
m
r A v
Example:
The water in the pipe of the previous example had a density of 62.44 lbm/ft3. Calculate
the mass flow rate.
Solution:
m
r
V
m
(62.44lbm
ft3
) (1.22
ft3
sec
)
m
76.2lbm
sec
Conservation of Mass
In thermodynamics, you learned that energy can neither be created nor destroyed, only changed
in form. The same is true for mass. Conservation of mass is a principle of engineering that
states that all mass flow rates into a control volume are equal to all mass flow rates out of the
control volume plus the rate of change of mass within the control volume. This principle is
expressed mathematically by Equation 3-4.
(3-4)
min
mout
Dm
Dt
where:
=
the increase or decrease of the mass within the control volume over a
Dm
Dt
(specified time period)
Steady-State Flow
Steady-state flow refers to the condition where the fluid properties at any single point in the
system do not change over time. These fluid properties include temperature, pressure, and
velocity. One of the most significant properties that is constant in a steady-state flow system is
the system mass flow rate. This means that there is no accumulation of mass within any
component in the system.
HT-03
Page 10
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