Conservation of Mass
In the Reynolds transport theorem for conservation of mass, let B = m, i.e. B_{sys} = m_{sys} = mass of the system,
For our system, we know that
So, Reynold's Transport Theorem (R.T.T.) becomes
OR,
Consider an outlet:
….since the negative sign is accounted for in
the conservation of mass equation,
i.e.
If an inlet or exit is not 1-D, we can still
use but V_{AV} must be the average
velocity
but for most problems V is parallel to n……
An equivalent 1-D outlet will have the same mass flow
rate as the actual outlet.
A container of water,
Given: V_{AV},
Q_{3}, D_{1}, D_{2} and h equal constants.
V_{1} = 3 m/s; Q_{3} = 0.01 m^{3}/s; h = constant;
D_{1} = 0.05m; D_{2}= 0.07m
Find: Average exit velocity V_{2 }
Solution: Use conservation
of mass. First draw the C.V. shown.
Since it is steady and incompressible,