Page 107 - Aeronautical Engineer Data Book
P. 107
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If fluid velocity increases in the x direction, it must decrease in the y direction (see Figure 5.3). A rotating or spinning element of fluid can be investigated by assuming it is a solid (see
or, in polar ∂q t 0 = ∂ or, in polar: ∂q n 1 ∂ r
= 0 1 + r
= ∂q t – ∂r Velocity at a point is given by: ∂ v = ∂x Velocity at a point is given by: ∂ v = ∂y
∂u + ∂v ∂y ∂x ∂q n q n + ∂r r ∂u ∂v – ∂y ∂x q t +
= r ∂ u = ∂y ∂
u = ∂x
Equation of continuity in 2D (incompressible flow) Equation of vorticity Stream function (incompressible flow) Velocity potential
(irrotational 2D flow)
