Finite Volume Analysis: Application
of Conservation of Linear Momentum
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Example 3 (continued) |
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The
equation for conservation of mass is: ∂/∂t
∫ ρ dV
+ ∫ ρ V • n dS = 0 cv cs For
steady flow the first integral is zero.
The second integral becomes: ρ V1 • n1 A1 + ρ
V2 • n2 A2 + ρ V3 • n3 A3 = 0 where n1 =
˗ i
, n2 = cos θ i + sin θ j , n3 = ˗cos
θ i ˗ sin θ j V1 = V1 i, V2 = V2
n2 , V3 = V3
n3 and
V1 = V2 = V3 = Vj where Vj = the
speed of the air jet So
for conservation of mass: ˗ ρ Vj A1 +
ρ Vj A2 +
ρ Vj A3 = 0 (1) |
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The
equation for conservation of linear momentum is: ∂/∂t
∫ ρ V dV + ∫
V ρ V • n
dS
= ∑ F cv cs |
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