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Finite Volume Analysis: Selection of Control Surface or Surfaces

Control Surface and Control Volume

for conservation of Mass Application

where CS is the control surface

CV is the control volume

n₁, n₂, n₃ are the unit outer normal vectors to the control surface

A₁, A₂, A₃ are the areas at stations 1, 2, and 3

V₁ is the velocity of the fluid entering the control surface

V₂, V₃ are the velocities of the fluid leaving the control surface

ρ is the density of the fluid

θ is the angle at station 3

Rate of mass flow in at station 1 equals rate of mass flow out at stations 2 and 3