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Unformatted text preview: from a pipe in the space ﬁlled with the same liquid, cf. ﬁgure 2) in a half-plane x > 0,-∞ < y < + ∞ : uu x + v u y = u yy , u x + v y = 0 , | u | → , y → ±∞ . Here ( u,v ) is the velocity ﬁeld with ( x,y )-components, respectively. ME220A 2 u v Figure 2: Submerged jet. Problem 6. Using aﬃne transforms, ﬁnd the solution for an axisymmetric drop spreading on a ﬂat surface, cf. ﬁgure 3, described by the following equation ∂h ∂t = 2 3 r ∂ ∂r ± rh 3 ∂h ∂r ² , with the boundary condition h = 0 at r = ∞ and a mass conservation condition, i.e. mass of the drop should be constant. Make use of a physically relevant conservation law. Determine short and long-time behavior of the solution. h(r,t) r h(r,t) Figure 3: Spreading drop....
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- Fall '10
- Kinetic theory, aﬃne transforms, axisymmetric drop spreading, potential unsteady ﬂow