# In deriving the continuity equation, we assumed, for simplicity,that the mass fl ow per unit area on the left face wasjust ρ u . In fact, ρ u varies also with y and z , and thus it mustbe different on the four corners of the left face. Account forthese variations, average the four corners, and determinehow this might change the inlet mass fl ow from ρ u dy dz .

Question

In deriving the continuity equation, we assumed, for simplicity,
that the mass fl ow per unit area on the left face was
just ρ u . In fact, ρ u varies also with y and z , and thus it must
be different on the four corners of the left face. Account for
these variations, average the four corners, and determine
how this might change the inlet mass fl ow from ρ u dy dz .

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Engineering
Mechanical Engineering